Indefinite Integration
AP EAPCET / Mathematics / Calculus / 147 questions
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Practice 147 AP EAPCET Mathematics questions from Indefinite Integration. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
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Indefinite Integration Questions
Showing 47 of 147 questions on this page.
1Indefinite Integration
If $\int \frac{\log \left(1+x^4\right)}{x^3} d x=f(x) \log \left(\frac{1}{g(x)}\right)+\tan ^{-1}$
$(h(x))+c$, then $h(x)\left[f(x)+f\left(\frac{1}{x}\right)\right]=$
$(h(x))+c$, then $h(x)\left[f(x)+f\left(\frac{1}{x}\right)\right]=$
MCQ+1 / -02024
2Indefinite Integration
\(\int\left(\frac{x}{x \cos x-\sin x}\right)^2 d x=\)
MCQ+1 / -02024
3Indefinite Integration
$\int e^{2 x+3} \sin 6 x d x=$
MCQ+1 / -02024
4Indefinite Integration
$\int \frac{\operatorname{cosec} x}{3 \cos x+4 \sin x} d x=$
MCQ+1 / -02024
5Indefinite Integration
$\int\left(\tan ^9 x+\tan x\right) d x=0$
MCQ+1 / -02024
6Indefinite Integration
$\int \frac{x+1}{\sqrt{x^2+x+1}} d x=$
MCQ+1 / -02024
7Indefinite Integration
$\int \frac{1}{x^5 \sqrt[3]{x^3+1}} d x=$
MCQ+1 / -02024
8Indefinite Integration
\(\int e^x\left(\frac{2+\sin 2 x}{1+\cos 2 x}\right) d x=\)
MCQ+1 / -02023
9Indefinite Integration
If $f(x)=\int \frac{d x}{\left(x^2+2\right)}$ and $f(\sqrt{2})=0$, then $f(0)=$
MCQ+1 / -02023
10Indefinite Integration
If $\frac{2 x^2+5 x+6}{(x+2)^3}=\frac{a}{x+2}+\frac{b}{(x+2)^2}+\frac{c}{(x+2)^3}$, then $a \cdot b+b \cdot c+c \cdot a=$
MCQ+1 / -02023
11Indefinite Integration
If $\int \frac{4 e^x+6 e^{-x}}{9 e^x-4 e^{-x}} d x=A x+B \log \left|\left(9 e^{2 x}-4\right)\right|+C$, then $(A, B)=$
MCQ+1 / -02023
12Indefinite Integration
If $\int \frac{1}{x\left[(\log x)^2+4 \log x-1\right]} d x=A \log \left[\frac{\log x+B}{\log x+C}\right]+K$,
where $K$ is the constant of integration, then
where $K$ is the constant of integration, then
MCQ+1 / -02023
13Indefinite Integration
$\int \frac{d x}{4+5 \cos x}=$
MCQ+1 / -02023
14Indefinite Integration
\(\int x^3(\log x)^2 d x=\)
MCQ+1 / -02023
15Indefinite Integration
If $f(x)=\int \frac{5 x^8+7 x^6}{\left(x^2+2 x^7+1\right)^2} d x(x \geq 0)$ and $f(0)=0$, then the value of $f(1)=$
MCQ+1 / -02023
16Indefinite Integration
If $\frac{x+2}{x^2-3}$ is one of the partial fractions of $\frac{3 x^3-x^2-2 x+17}{x^4+x^2-12}$, then the other partial fraction of it is
MCQ+1 / -02023
17Indefinite Integration
If \(I_n=\int\left(\cos ^n x+\sin ^n x\right) d x\) and \(I_n-\frac{n-1}{n} I_{n-2} =\frac{\sin x \cos x}{n} f(x)\), then \(f(x)=\)
MCQ+1 / -02022
18Indefinite Integration
\(\int \frac{d x}{(x-3)^{\frac{4}{5}}(x+1)^{\frac{6}{5}}}=\)
MCQ+1 / -02022
19Indefinite Integration
\(\int \frac{e^{\tan ^{-1} x}}{1+x^2}\left[\left(\sec ^{-1} \sqrt{1+x^2}\right)^2+\cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right)\right] d x=\)
MCQ+1 / -02022
20Indefinite Integration
\(\int \frac{3 x+4}{x^3-2 x+4} d x=\log f(x)+C \Rightarrow f(3)=\)
MCQ+1 / -02022
21Indefinite Integration
\(\frac{2 x^2+1}{x^3-1}=\frac{A}{x-1}+\frac{B x+C}{x^2+x+1} \Rightarrow 7 A+2 B+C=\)
MCQ+1 / -02022
22Indefinite Integration
\(\int \frac{e^{\cot x}}{\sin ^2 x}(2 \log \operatorname{cosec} x+\sin 2 x) d x=\)
MCQ+1 / -02022
23Indefinite Integration
The parametric form of a curve is \(x=\frac{t^3}{t^2-1} y=\frac{t}{t^2-1}\), then \(\int \frac{d x}{x-3 y}=\)
MCQ+1 / -02022
24Indefinite Integration
If \(I_n=\int \tan ^n x d x\), and \(I_0+I_1+2 I_2+2 I_3+2 I_4 +I_5+I_6=\sum_\limits{k=1}^n \frac{\tan ^k x}{k}\), then \(n=\)
MCQ+1 / -02022
25Indefinite Integration
Assertion (A) If \(I_n=\int \cot ^n x d x\), then
\(I_6+I_4=\frac{-\cot ^5 x}{5}\)
Reason (R) \(\int \cot ^n x d x=\frac{-\cot ^{n-1} x}{n} -\int \cot ^{n-2} x d x\)
\(I_6+I_4=\frac{-\cot ^5 x}{5}\)
Reason (R) \(\int \cot ^n x d x=\frac{-\cot ^{n-1} x}{n} -\int \cot ^{n-2} x d x\)
MCQ+1 / -02022
26Indefinite Integration
\(\int \frac{1+\tan x \tan (x+a)}{\tan x \tan (x+a)} d x=\)
MCQ+1 / -02022
27Indefinite Integration
If \(\int \frac{1+\sqrt{\tan x}}{\sin 2 x} d x=A \log \tan x+B \tan x+C\), then \(4 A-2 B=\)
MCQ+1 / -02022
28Indefinite Integration
If \(f(x)=\int x^2 \cos ^2 x\left(2 x \tan ^2 x-2 x-6 \tan x\right) d x\) and \(f(0)=\pi\), then \(f(x)=\)
MCQ+1 / -02022
29Indefinite Integration
If
\(\int \frac{e^{\sqrt{x}}}{\sqrt{x}}(x+\sqrt{x}) d x=e^{\sqrt{x}}[A x+B \sqrt{x}+C]+K\) then \(A+B+C=\)
\(\int \frac{e^{\sqrt{x}}}{\sqrt{x}}(x+\sqrt{x}) d x=e^{\sqrt{x}}[A x+B \sqrt{x}+C]+K\) then \(A+B+C=\)
MCQ+1 / -02022
30Indefinite Integration
If \(\int \frac{(2 x+1)^6}{(3 x+2)^8} d x=P\left(\frac{2 x+1}{3 x+2}\right)^Q+R\), then \(\frac{P}{Q}\) is equal to
MCQ+1 / -02021
31Indefinite Integration
If \(\int\left[\cos (x) \cdot \frac{d}{d x}(\operatorname{cosec}(x)] d x=f(x)+g(x)+c\right.\) then \(f(x) \cdot g(x)\) is equal to
MCQ+1 / -02021
32Indefinite Integration
If \(\int \frac{\cos 4 x+1}{\cot x-\tan x}=k \cos 4 x+C\), then \(k\) is equal to
MCQ+1 / -02021
33Indefinite Integration
\(\int \frac{\sin \alpha}{\sqrt{1+\cos \alpha}} d \alpha\) is equal to
MCQ+1 / -02021
34Indefinite Integration
Given, \(\frac{3 x-2}{(x+1)^2(x+3)}=\frac{A}{x+1} +\frac{B}{(x+1)^2}+\frac{C}{x+3}\), then \(4 A+2 B+4 C\) is equal to
MCQ+1 / -02021
35Indefinite Integration
\(\int \frac{\sec x}{\sqrt{\sin (2 x+\theta)+\sin \theta}} d x\) is equal to
MCQ+1 / -02021
36Indefinite Integration
If the primitive of \(\cos (\log x)\) is \(f(x)\{\cos (g(x))+\sin (h(x))\}\), then which among the following is true?
MCQ+1 / -02021
37Indefinite Integration
If \(f(x)=\frac{1}{\left(\cos ^2 x\right) \sqrt{1+\tan x}}\), then its antiderivative \(F(x)=\) ........, given, \(F(0)=4\)
MCQ+1 / -02021
38Indefinite Integration
If \(f^{\prime}(x)=x+\frac{1}{x}\), then \(f(x)\) is equal to
MCQ+1 / -02021
39Indefinite Integration
If
$$\begin{aligned} \frac{2 x^4-x^3+3 x^2-x+4}{x^2-3 x+2} =f(x)+\frac{A}{x-1}+\frac{B}{x-2}\end{aligned}$$, then
$$\begin{aligned} \frac{2 x^4-x^3+3 x^2-x+4}{x^2-3 x+2} =f(x)+\frac{A}{x-1}+\frac{B}{x-2}\end{aligned}$$, then
MCQ+1 / -02021
40Indefinite Integration
If \(\int \frac{1-(\cot x)^{2021}}{\tan x+(\cot x)^{2022}} d x=\frac{1}{A} \log\left|(\sin x)^{2023}+(\cos x)^{2023}\right|+c\), then \(A\) is equal to
MCQ+1 / -02021
41Indefinite Integration
If \(\int \frac{(x-1)^2}{\left(x^2+1\right)^2} d x=\tan ^{-1}(x)+g(x)+k\), then \(g(x)\) is equal to
MCQ+1 / -02021
42Indefinite Integration
\(\int \frac{e^x(x+3)}{(x+5)^3} d x\) is equal to
MCQ+1 / -02021
43Indefinite Integration
If \(\int \frac{1}{1+\sin x} d x=\tan (f(x))+c\), then \(f^{\prime}(0)\) is equal to
MCQ+1 / -02021
44Indefinite Integration
\(\int \sqrt{e^{4 x}+e^{2 x}} d x\) is equal to
MCQ+1 / -02021
45Indefinite Integration
\(\int(\cos x) \log \cot \left(\frac{x}{2}\right) d x\) is equal to
MCQ+1 / -02021
46Indefinite Integration
\(\int \frac{1+x+\sqrt{x+x^2}}{\sqrt{x}+\sqrt{1+x}} d x\) is equal to
MCQ+1 / -02021
47Indefinite Integration
Which of the following is partial fraction of \(\frac{-x^2+6 x+13}{(3 x+5)\left(x^2+4 x+4\right)}\) is equal to
MCQ+1 / -02021
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