Indefinite Integration PYQs - Last 10 Years

AP EAPCET / Mathematics / Calculus / 147 recent questions

MathematicsCalculus2016-2025

All Indefinite Integration PYQs Last 5 Years Create chapter test

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.

147

PYQs on Page

Mathematics / Calculus

2021-2025

Year Range

Based on indexed question metadata

147

Last 5 Years

2021-2025

147

Last 10 Years

2016-2025

Recent Year Trend

2021

2022

2023

2024

2025

202157 max PYQs/year2025

Question Types

147PYQs

MCQ100%

Difficulty Mix

#1 Unknown147

147 in last 5 years147 in last 10 years

Last 10 Years Indefinite Integration Questions

Showing 50 of 147 filtered questions.

1Indefinite Integration

If $\int \frac{x}{x \tan x+1} d x=\log f(x)+k$, then $f\left(\frac{\pi}{4}\right)=$

2Indefinite Integration

\(\int \sin ^{-1}\left(\sqrt{\frac{x}{a+x}}\right) d x=\)

3Indefinite Integration

\(\int \frac{d x}{(1+\sqrt{x}) \sqrt{x-x^2}}=\)

4Indefinite Integration

\(\int x \cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right) d x(x>0)=\)

5Indefinite Integration

If $\int \frac{5 \tan x}{\tan x-2} d x=a x+b \log |\sin x-2 \cos x|+c$, then $a+b=$

6Indefinite Integration

If $\frac{x^2}{\left(x^2+2\right)\left(x^4-1\right)}=\frac{A}{x^2-1}+\frac{B}{x^2+1}+\frac{C}{x^2+2}$, then $A+B-C=$

7Indefinite Integration

If $\int \frac{x^4+1}{x^2+1} d x=A x^3+B x^2+C x+D \tan ^{-1} x+E$, then $A+B+C+D=$

8Indefinite Integration

If $\int \frac{d x}{1-\sin ^4 x}=A \tan x+B \tan ^{-1}(\sqrt{2} \tan x)+C$, then $A^2-B^2=$

9Indefinite Integration

If $\int \frac{a \cos x+3 \sin x}{5 \cos x+2 \sin x} d x=\frac{26}{29} x-\frac{k}{29} \log |5 \cos x+2 \sin x|+\ldots$ then $|a+k|=$

10Indefinite Integration

If $\frac{x^4}{(x-1)(x-2)}=f(x)+\frac{A}{x-1}+\frac{B}{x-2}$, then $f(-2)+A+B=$

11Indefinite Integration

\(\int \sec \left(x-\frac{\pi}{3}\right) \sec \left(x+\frac{\pi}{6}\right) d x=\)

12Indefinite Integration

$$ \begin{aligned} & \text { If } \int \frac{x^2-x+2}{x^2+x+2} d x=x-\log (f(x))+\frac{2}{\sqrt{7}} \tan ^{-1}(g(x))+c, \text { then } \\ & f(-1)+\sqrt{7} g(-1)= \end{aligned} $$

13Indefinite Integration

\(\int \frac{1}{1+x+x^2} d x=\)

14Indefinite Integration

If $\frac{2 x^4-3 x^2+4}{\left(x^2+1\right)\left(x^2+2\right)}=a+\frac{p x+q}{x^2+1}+\frac{m x+n}{x^2+2}$, then $\frac{n}{q}=$

15Indefinite Integration

\(\int \sin ^3 x \cos ^2 x d x=\)

16Indefinite Integration

\(\int \frac{x+1}{(x-2) \sqrt{1-x}} d x=\)

17Indefinite Integration

If $\int \frac{d x}{(x \tan x+1)^2}=f(x)+C$, then $\lim\limits_{x \rightarrow \frac{\pi}{2}} f(x)=$

18Indefinite Integration

\(\int(\log 2 x)^3 d x=\)

19Indefinite Integration

For $0 < x < 1, \int\left[\tan ^{-1}\left(1-x+x^2\right)+\tan ^{-1}(1-x)\right] d x=$

20Indefinite Integration

$\int \frac{\sqrt{x-2}}{2 x+4} d x=$

21Indefinite Integration

\(\int \frac{x}{\sqrt{x^2-2 x+5}} d x=\)

22Indefinite Integration

If $\frac{3 x^3-7 x+1}{(x-2)^5}=\frac{A}{x-2}+\frac{B}{(x-2)^2}+\frac{C}{(x-2)^3}+\frac{D}{(x-2)^4}+\frac{E}{(x-2)^5}, \text { then } A(B+C+D+E)= $

23Indefinite Integration

If $\int x^{49}\left[\tan ^{-1} x^{50}+\frac{x^{50}}{1+x^{100}}\right] d x=\frac{x^n}{k} f(x)+c$, then
\(f(x)-f\left(\sqrt[k]{x^n}\right)=\)

24Indefinite Integration

\(\int(\sqrt{\tan x}+\sqrt{\cot x}) d x=\)

25Indefinite Integration

\(\int \frac{x+1}{x^3-1} d x=\)

26Indefinite Integration

\(\int \frac{\sec ^2 x}{(\sec x+\tan x)^{\frac{5}{2}}} d x=\)

27Indefinite Integration

\(\int \frac{x^4-16 x^2+2 x+8}{x^3-4 x^2+2} d x=\)

28Indefinite Integration

\(\int \frac{1}{\cos x}\left[\frac{1}{\sin x}-\frac{1}{\sin x+3 \cos x}\right] d x=\)

29Indefinite Integration

\(\int \cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right) d x=\)

30Indefinite Integration

If $\int \frac{d x}{2 \cos x+3 \sin x+4}=\frac{2}{\sqrt{3}} f(x)+C$, then $f\left(\frac{2 \pi}{3}\right)=$

31Indefinite Integration

\(\int \frac{d x}{(x+1) \sqrt{x^2+1}}=\)

32Indefinite Integration

If $\int \frac{1}{\left((x+4)^3(x+1)^5\right)^{1 / 4}} d x=A \cdot\left(\frac{x+4}{x+1}\right)^n+C$

33Indefinite Integration

If $\int\left(x^6+x^4+x^2\right) \sqrt{2 x^4+3 x^2+6} d x=f(x)+c$, then $f(3)=$

34Indefinite Integration

\(\int \frac{\sec ^2 x}{\sin ^7 x} d x-\int \frac{7}{\sin ^7 x} d x=\)

35Indefinite Integration

If $\frac{3 x+1}{(x-1)\left(x^2+2\right)}=\frac{A}{x-1}+\frac{B x+C}{x^2+2}$, then $5(A-B)=$

36Indefinite Integration

\(\int \frac{(3 x-2) \tan \left(\sqrt{9 x^2-12 x+1}\right)}{\sqrt{9 x^2-12 x+1}} d x=\)

37Indefinite Integration

\(\int \frac{x^4-1}{x^2 \sqrt{x^4+x^2+1}} d x=\)

38Indefinite Integration

\(\int \frac{\sin x+\cos x}{\sin x-\cos x} d x=\)

39Indefinite Integration

\(\int \frac{1}{9 \cos ^2 x-24 \sin x \cos x+16 \sin ^2 x} d x=\)

40Indefinite Integration

If $\int \frac{1}{\cot \frac{x}{2} \cot \frac{x}{3} \cot \frac{x}{6}} d x=A \log \left|\cos \frac{x}{2}\right| +B \log \left|\cos \frac{x}{3}\right|+C \log \left|\cos \frac{x}{6}\right|+k$, then $A+B+C=$

41Indefinite Integration

If $\frac{x+1}{(x-1)^2\left(x^2+1\right)}=\frac{A}{x-1}+\frac{B}{(x-1)^2}+\frac{C x+D}{x^2+1}$, then $\sqrt{3 A^2+4 D^2+5 C^2+B^2}=$

42Indefinite Integration

\(\int \sqrt{x^2+x+1} d x\)

43Indefinite Integration

\(\int \frac{13 \cos 2 x-9 \sin 2 x}{3 \cos 2 x-4 \sin 2 x} d x=\)

44Indefinite Integration

If $\int \frac{\cos ^3 x}{\sin ^2 x+\sin ^4 x} d x=c-\operatorname{cosec} x-f(x)$, then $f\left(\frac{\pi}{2}\right)=$

45Indefinite Integration

\(\int \frac{d x}{12 \cos x+5 \sin x}=\)

46Indefinite Integration

\(\int\left(\sum_{r=0}^{\infty} \frac{x^r 2^r}{r!}\right) d x=\)

47Indefinite Integration

If $\frac{a x+5}{\left(x^2+b\right)(x+3)}=\frac{x+21}{12\left(x^2+b\right)}+\frac{c}{12(x+3)}$, then $b^2=$

48Indefinite Integration

$\int\left(\frac{1+x+\sqrt{x+x^2}}{\sqrt{x}+\sqrt{1+x}}\right) d x=$

49Indefinite Integration

\(\int \frac{x}{\left(1-x^2\right) \sqrt{2-x^2}} d x=\)

50Indefinite Integration

If $\int x^2 \cos ^2 x d x=\frac{1}{6} f(x)+g(x) \sin 2 x +h(x) \cos 2 x+c$, then $f(1)+g(2)+h\left(\frac{1}{2}\right)=$