Indefinite Integration PYQs - Last 10 Years

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Practice 41 COMEDK Mathematics questions from Indefinite Integration. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

41

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Mathematics / Calculus

2020-2026

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35

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2022-2026

41

Last 10 Years

2017-2026

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35 in last 5 years41 in last 10 years

Last 10 Years Indefinite Integration Questions

Showing 41 of 41 filtered questions.

1Indefinite Integration

\(\int \frac{x+1}{x\left(1+x e^x\right)} d x=\)

2Indefinite Integration

\(\int \sqrt{2 a x-x^2} d x=\)

3Indefinite Integration

\(\int e^{2 x} \cos (5 x+3) d x=\)

4Indefinite Integration

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

5Indefinite Integration

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

6Indefinite Integration

\(\int\left(\sin ^6 x+\cos ^6 x+3 \sin ^2 x \cos ^2 x\right) d x=\)

7Indefinite Integration

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

8Indefinite Integration

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

9Indefinite Integration

$\int \log x^2 d x=$

10Indefinite Integration

$\int \frac{d x}{(x+2)\left(x^2+1\right)}=p \log |x+2|+q \log \left|x^2+1\right|+r \tan ^{-1} x+c$ then $p+q+r=$

11Indefinite Integration

$\int \tan ^2\left(5-\frac{x}{2}\right) d x=$

12Indefinite Integration

$\int \frac{1}{\sqrt{9+8 x-x^2}} d x=\varphi(x)+c$ then $\varphi(x)=$

13Indefinite Integration

$\int\left(e^{x \log _e 6}\right) e^x d x=\phi(x)+c$ then $\phi(x)=$

14Indefinite Integration

\(\int \frac{\sin 2 x}{(1+\sin x)(2+\sin x)} d x=a \log |1+\sin x|-b \log |2+\sin x|+c\)
then the value of $a$ and $b$ is ----------------

15Indefinite Integration

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

16Indefinite Integration

$\int \frac{\sin x+\cos x}{\sqrt{1+2 \sin x \cos x}} d x=\varphi(x)+C$ Then $\varphi(x)=$

17Indefinite Integration

$\int \frac{x}{(x-1)(x-2)^2} d x=a \log \left|\frac{x-1}{x-2}\right|+\frac{b}{(x-2)}+c$ then

18Indefinite Integration

$\int \frac{d x}{x \sqrt{4 x^2-9}}=$

19Indefinite Integration

\(\int \frac{x}{x^4-16} d x=\)

20Indefinite Integration

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

21Indefinite Integration

If \(\int \frac{1}{\sqrt{\sin ^3 x \cos x}} d x=\frac{k}{\sqrt{\tan x}}+c\) then the value of \(k\) is

22Indefinite Integration

\(\text { The value of } \int \frac{1}{x+\sqrt{x-1}} d x \text { is }\)

23Indefinite Integration

\(\text { The value of } \int \frac{d x}{\sqrt{2 x-x^2}} \text { is }\)

24Indefinite Integration

\(\int e^x\left[\frac{x^2+1}{(x+1)^2}\right] d x \quad \text { is equal to }\)

25Indefinite Integration

\(\int \log x(\log x+2) d x \text { equals to }\)

26Indefinite Integration

\(\int \frac{f^{\prime}(x)}{f(x) \log (f(x))} d x \text { is equal to }\)

27Indefinite Integration

\(\int \frac{1+x+\sqrt{x+x^2}}{\sqrt{x}+\sqrt{1+x}} d x \text { is equal to }\)

28Indefinite Integration

\(\int \frac{\cos 4 x+1}{\cot x-\tan x} d x=\)

29Indefinite Integration

\(\int \sqrt{\operatorname{cosec} x-1} d x=\)

30Indefinite Integration

\(\int e^x\left(1+\tan x+\tan ^2 x\right) d x \text { is equal to }\)

31Indefinite Integration

\(\int x^x(1+\log x) d x\) is equal to

32Indefinite Integration

\(\int \frac{4^x}{\sqrt{1-16^x}} d x\) is equal to

33Indefinite Integration

\(\int \frac{x d x}{2(1+x)^{3 / 2}}\) is equal to

34Indefinite Integration

\(\int \frac{3^x}{\sqrt{1-9^x}} d x\) is equal to

35Indefinite Integration

\(\int \frac{1}{x \sqrt{a x-x^2}} d x\) is

36Indefinite Integration

Integral of \(\int {{{dx} \over {{x^2}{{[1 + {x^4}]}^{3/4}}}}}\).

37Indefinite Integration

\(\int {{{{2^x}} \over {\sqrt {1 - {4^x}} }}dx}\) is equal to

38Indefinite Integration

The value of \(\int {{{{x^2} + 1} \over {{x^2} - 1}}dx}\) is

39Indefinite Integration

The value of \(\int {{e^x}({x^5} + 5{x^4} + 1)\,.\,dx}\) is

40Indefinite Integration

The value of \(\int {{1 \over {1 + \cos 8x}}dx}\) is

41Indefinite Integration

\({{3{x^2} + 1} \over {{x^2} - 6x + 8}}\) is equal to