Indefinite Integration PYQs - Last 5 Years
TS EAMCET / Mathematics / Calculus / 104 recent questions
MathematicsCalculus2021-2025
Practice 104 TS EAMCET Mathematics questions from Indefinite Integration. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
104
PYQs on Page
Mathematics / Calculus
2022-2025
Year Range
Based on indexed question metadata
104
Last 5 Years
2021-2025
104
Last 10 Years
2016-2025
Recent Year Trend
2022
2023
2024
2025Latest year
202228 max PYQs/year2025
Question Types
104PYQs
MCQ100%
Difficulty Mix
#1 Unknown104
104 in last 5 years104 in last 10 years
Last 5 Years Indefinite Integration Questions
Showing 50 of 104 filtered questions.
1Indefinite Integration
If $\int\left(1+x-x^{-1}\right) e^{\left(x+x^{-1}\right)} d x=f(x)+C$, then $f(1)-f(-1)=$
MCQ+1 / -02024
2Indefinite Integration
If $\int(\log x)^3 x^5 d x=\frac{x^6}{A}\left[B(\log x)^3\right. \left.+C(\log x)^2+D(\log x)-1\right]+k$ and $A, B, C, D$ are integers, then $A-(B+C+D)=$
MCQ+1 / -02023
3Indefinite Integration
$\int \frac{d x}{(x-1)^{\frac{3}{4}}(x+2)^{\frac{5}{4}}}=$
MCQ+1 / -02023
4Indefinite Integration
\(\int \frac{d x}{\left(x^2+1\right)\left(x^2+4\right)}=\)
MCQ+1 / -02023
5Indefinite Integration
If $\int \frac{x^{49} \tan ^{-1}\left(x^{50}\right)}{\left(1+x^{100}\right)} d x=k\left(\tan ^{-1}\left(x^{50}\right)\right)^2+C$, then $k=$
MCQ+1 / -02023
6Indefinite Integration
$$ \begin{aligned} & \text { If } \int \frac{1}{\operatorname{cosec} x+\cos x} d x=\frac{1}{2 \sqrt{3}} \log |f(x)| \\ & -\int \frac{\cos x-\sin x}{2+\sin 2 x} d x+c, \text { then at } x=\frac{\pi}{3},|f(x)|= \end{aligned} $$
MCQ+1 / -02023
7Indefinite Integration
\(\int \frac{1}{(x-1)^{\frac{5}{7}}(x+1)^{\frac{9}{7}}} d x=\)
MCQ+1 / -02023
8Indefinite Integration
$\int \frac{1+\sqrt{3} \cot x}{1-\sqrt{3} \cot x} d x=$
MCQ+1 / -02023
9Indefinite Integration
\(\int \frac{\tan x}{\sec ^2 x\left(1+\sec ^6 x\right)^{\frac{2}{3}}} d x=\)
MCQ+1 / -02023
10Indefinite Integration
\(\int \frac{1}{16-7 \sin ^2 x} d x=\)
MCQ+1 / -02023
11Indefinite Integration
\(\int \frac{\sec ^2 x}{(\sec x+\tan x)^2} d x=\)
MCQ+1 / -02023
12Indefinite Integration
\(\int \frac{1}{3 \cos x-4 \sin x+5} d x=\)
MCQ+1 / -02023
13Indefinite Integration
\(\int \frac{1}{(x-2)\left(x^2+1\right)} d x=\)
MCQ+1 / -02023
14Indefinite Integration
If $\frac{3 \pi}{2} < x < \frac{5 \pi}{2}$ and $\int(\sqrt{1-\sin x}+\sqrt{1+\sin x}) d x=f(x)+C$, where $C$ is the constant of integration, then $f\left(\frac{\pi}{3}\right)-f(0)=$
MCQ+1 / -02023
15Indefinite Integration
$\int \frac{2 x+3}{\sqrt{3 x^2-2 x+1}} d x=$
MCQ+1 / -02023
16Indefinite Integration
If $\int \frac{2 \sin 2 x-3 \cos x}{2 \sin ^2 x-3 \sin x+4} d x=f(x)+C$, where $C$ is the constant of integration, then $f\left(\frac{\pi}{2}\right)-f(0)=$
MCQ+1 / -02023
17Indefinite Integration
$\int \frac{1}{\left(x+\frac{2}{x}\right) \sqrt{x^4+4 x^2+3}} d x=$
MCQ+1 / -02023
18Indefinite Integration
If $\int \frac{x^2\left(\sec ^2 x+\tan x\right)}{(x \tan x+1)^2} d x=\frac{-x^2}{x \tan x+1}+f(x)+C$, then
\(f(x)=\)
\(f(x)=\)
MCQ+1 / -02023
19Indefinite Integration
If $\int e^x\left(\sin ^2 2 x-8 \cos 4 x\right) d x=e^x f(x)+C$, then $f\left(\frac{\pi}{4}\right)=$
MCQ+1 / -02023
20Indefinite Integration
If $\frac{x^4}{(x-1)(x-2)(x-3)}=p(x)+\frac{A}{x-1}+\frac{B}{x-2}+\frac{C}{x-3}$, then $p\left(\frac{3}{2}\right)+C=$
MCQ+1 / -02023
21Indefinite Integration
If $n$ is a positive integer greater than 1 and $I_n=\int \frac{\sin n x}{\sin x} d x$, then $I_{n+1}-I_{n-1}=$
MCQ+1 / -02023
22Indefinite Integration
7. If $\int \sin (101 x)(\sin x)^{99} d x$ $=\frac{\sin (100 x)(\sin x)^\lambda}{\mu}+C$ then, $\frac{\lambda}{\mu}=$
MCQ+1 / -02023
23Indefinite Integration
\(\int \frac{\sin ^8 x-\cos ^8 x}{1-2 \sin ^2 x \cos ^2 x} d x=\)
MCQ+1 / -02023
24Indefinite Integration
If $\int x^4(\log x)^3 d x=x^5\left[A(\log x)^3\right]$ $\left.+B(\log x)^2+C \log x+D\right]+k$, then $A+B+C+5 D=$
MCQ+1 / -02023
25Indefinite Integration
\(\text { Match the following items from List I into List II }\)
List-I
List-II
1.
∫
sin
2
x
cos
4
x...
List-I
List-II
1.
∫
sin
2
x
cos
4
x...
MCQ+1 / -02023
26Indefinite Integration
If $\frac{x+1}{\left(x^2+1\right)(x-1)^2}=\frac{A x+B}{x^2+1}+\frac{C}{x-1}+\frac{D}{(x-1)^2}$, then $A+B+C+D=$
MCQ+1 / -02023
27Indefinite Integration
If $\int \frac{x}{(a+x)^5} d x=\frac{1}{k(a+x)^4}(f(x))+C$, then $\frac{f(-a)}{a k}=$
MCQ+1 / -02023
28Indefinite Integration
If $\frac{2 x^2-3 x+5}{(x-7)^3}=\frac{A}{x-7}+\frac{B}{(x-7)^2}+\frac{C}{(x-7)^3}$, then $2 A-3 B+C=$
MCQ+1 / -02022
29Indefinite Integration
If $x \neq(2 n+1) \frac{\pi}{2}$, then $\int \frac{\cos ^3 x}{(1+\sin x)^4} d x=$
MCQ+1 / -02022
30Indefinite Integration
If $\frac{3 x^2+a x+3}{(2 x+3)\left(x^2+2\right)}=\frac{3}{2 x+3}+\frac{B x+C}{x^2+2}$, then $a(B+C)=$
MCQ+1 / -02022
31Indefinite Integration
If $\tan \alpha=\frac{4}{3}$, then $\int \frac{1}{3 \cos x-4 \sin x} d x=$
MCQ+1 / -02022
32Indefinite Integration
If $\frac{3 \pi}{4}
MCQ+1 / -02022
33Indefinite Integration
Given that $\int \frac{1}{x^2+a^2} d x=\frac{1}{a} \tan ^{-1}\left(\frac{x}{a}\right)+c$.
$$ \begin{aligned} & \text { If } \int \frac{1}{x^4+3 x^2+1} d x=a \tan ^{-1}\left(\frac{b\left(x^2-1\right)}{x}\right) \\ & +c \tan ^{-1}\left(\frac{...
$$ \begin{aligned} & \text { If } \int \frac{1}{x^4+3 x^2+1} d x=a \tan ^{-1}\left(\frac{b\left(x^2-1\right)}{x}\right) \\ & +c \tan ^{-1}\left(\frac{...
MCQ+1 / -02022
34Indefinite Integration
If $f(x)=\int \frac{2-3 \sin ^2 x}{1+\cos 2 x} d x$ and $f\left(\frac{\pi}{4}\right)=1$, then $f(0)=$
MCQ+1 / -02022
35Indefinite Integration
If $x \neq(2 n+1) \frac{\pi}{2}, n \in Z$ and $\cos x \neq \frac{-1}{2}$, then
\(\int\left(\frac{\sin x+\sin 2 x}{1+\cos x+\cos 2 x}\right)^2 d x=\)
\(\int\left(\frac{\sin x+\sin 2 x}{1+\cos x+\cos 2 x}\right)^2 d x=\)
MCQ+1 / -02022
36Indefinite Integration
If $\frac{x^2-x+1}{\left(x^2+1\right)\left(x^2+x+1\right)}=\frac{A x+B}{x^2+1}+\frac{C x+D}{x^2+x+1}$, then $A+2 B+C+2 D=$
MCQ+1 / -02022
37Indefinite Integration
If $\frac{x-2}{x^2(2 x-3)}=\frac{A}{x}+\frac{B}{x^2}+\frac{C}{2 x-3}$, then $2(A-C)=$
MCQ+1 / -02022
38Indefinite Integration
Given that $\frac{d}{d x}\left(\tan ^{-1} x\right)=\frac{1}{1+x^2}$ and $\frac{d}{d x}\left(\sin h^{-1} x\right)=\frac{1}{\sqrt{1+x^2}}$. Then, $\int \frac{3 x^6-2 x^4+x^2-2}{x^2+1} d x=$
MCQ+1 / -02022
39Indefinite Integration
If $f(x)=\int \frac{16 x^7+5 x^{10}}{\left(x^3+2+3 x^8\right)^2} d x(x \geq 0)$ and $f(0)=1$, then the value of $f(-1)$ is
MCQ+1 / -02022
40Indefinite Integration
\(\int \frac{\sin x \cdot \sec ^2 x-\tan x \cdot \sin x+\cos x}{(1-\cos 2 x)} d x=\)
MCQ+1 / -02022
41Indefinite Integration
If $\frac{42-13 x}{x^2+x-6}=\frac{A}{l x+m}+\frac{B}{p x+q}$, where $l m>0$ and $p q<0$, then $\frac{A l p}{B m q}=$
MCQ+1 / -02022
42Indefinite Integration
If $f(x)=\int\left[\tan ^2 x+\cot ^2 x+\frac{4\left(\sin ^3 x+\cos ^3 x\right)}{\sin ^2 2 x}\right] d x$ and $f\left(\frac{\pi}{4}\right)=0$, then $3\left[f\left(\frac{\pi}{6}\right)+2\right]=$
MCQ+1 / -02022
43Indefinite Integration
$\int \sqrt{4 \cos ^2 x-5 \sin ^2 x} \cos x d x=$
MCQ+1 / -02022
44Indefinite Integration
If $\frac{x^2-2}{\left(x^2+1\right)\left(x^2+3\right)}=\frac{A x+B}{x^2+1}+\frac{C x+D}{x^2+3}$, then $D=$
MCQ+1 / -02022
45Indefinite Integration
Let $g(x)$ be the anti-derivative of $f(x)$. Then, the function for which $\log _e\left(1+(g(x))^2\right)+c$ is an anti-derivative is
MCQ+1 / -02022
46Indefinite Integration
If $\frac{x^2-3 x+2}{(x-4)(x-3)^2}=\frac{A}{x-4}+\frac{B}{x-3}+\frac{C}{(x-3)^2}$ then $A+B+C=$
MCQ+1 / -02022
47Indefinite Integration
\(\int(2 x-3) \sqrt{3 x+2} d x=\)
MCQ+1 / -02022
48Indefinite Integration
If $\frac{x^2+3}{\left(x^2+1\right)\left(x^2+2\right)}=\frac{A x+B}{x^2+1}+\frac{C x+D}{x^2+2}$ then $A+B+C+D=$
MCQ+1 / -02022
49Indefinite Integration
Let $f(x)=\int \frac{2 x^3-3 x^2+4 x-5}{x^2} d x$ and $f(1)=1$. Then, $f(5)=$
MCQ+1 / -02022
50Indefinite Integration
If $x>0$ and $x \neq(2 n+1) \frac{\pi}{2}$, then $\int\left(x \sqrt{x}-e^{\log (\sec x \tan x)}+\frac{3 x^2-2 x+1}{x^2}\right) d x=$
MCQ+1 / -02022