Indefinite Integration PYQs - Last 10 Years

MHT CET / Mathematics / Calculus / 267 recent questions

MathematicsCalculus2017-2026

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Practice 267 MHT CET 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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Last 10 Years Indefinite Integration Questions

Showing 50 of 267 filtered questions.

1Indefinite Integration

If $\int \dfrac{x+1}{x^2+1}dx = \tan^{-1}x + g(x) + c$, where $c$ is constant of integration, then the function $g(x)$ is monotonically increasing in the interval

2Indefinite Integration

$\int \dfrac{(x+1)}{x(1+xe^x)^2}dx =$

3Indefinite Integration

If $\int x^2 \cdot e^x dx = e^x f(x) + c$, then the minimum value of $f(x)$ is ...

4Indefinite Integration

$\int \dfrac{x}{x + 2} dx$ is equal to

5Indefinite Integration

If $\int \dfrac{dx}{\sqrt{2ax - x^2}} = f(g(x)) + c$, where $c$ is constant of integration, then $f(x), g(x)$ are respectively equal to

6Indefinite Integration

$\int \dfrac{x + 2}{x^2 - 7x + 12} dx$ is equal to

7Indefinite Integration

$\int \dfrac{2x}{4 - 3x - x^2} dx = \cdots$

8Indefinite Integration

The value of $\int \dfrac{1}{x^2 - 5x + 8} dx$ is equal to...

9Indefinite Integration

$\int \sqrt{4^x(4^x + 4)}\, dx = \cdots$

10Indefinite Integration

$\int \dfrac{\sin x}{\sin 4x} dx = $

11Indefinite Integration

$\int \frac{\sin 7 x}{\cos 9 x \cos 2 x} \mathrm{~d} x$ is equal to

12Indefinite Integration

If $A=\left[\begin{array}{lll}a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c\end{array}\right]$ where $a=7^x, b=7^{7^x}, c=7^{7^{7^x}}$ then $\int|A| d x$, (Where $|A|$ is the determinant of the matrix $A$ ) is equal to

13Indefinite Integration

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

14Indefinite Integration

If $\int \frac{\mathrm{d} x}{x^4+5 x^2+4}=\mathrm{A} \tan ^{-1} x+\mathrm{B} \tan ^{-1} \frac{x}{2}+\mathrm{c}$ where c is a constant of integration, then

15Indefinite Integration

\(\int \frac{\sqrt{\tan x}}{\sin x \cdot \cos x} d x=\)

16Indefinite Integration

If $\int \frac{\left(x^4+1\right)}{x\left(x^2+1\right)^2} d x=A \log |x|+\frac{B}{1+x^2}+c$, then $\mathrm{A}-\mathrm{B}$ is (where c is the constant of integration)

17Indefinite Integration

\(\int \frac{\mathrm{d} x}{\sin ^2 x \cos ^2 x}=\)

18Indefinite Integration

\(\int \frac{\mathrm{d} x}{x^{\frac{1}{2}}+x^{\frac{1}{3}}}=\mathrm{A} x^{\frac{1}{2}}+\mathrm{B} x^{\frac{1}{3}}+\mathrm{C} x^{\frac{1}{6}}+\mathrm{D} \log \left(x^{\frac{1}{6}}+1\right)+\mathrm{k}\)
(where k is the integration constant)...

19Indefinite Integration

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

20Indefinite Integration

$\int \mathrm{e}^x\left(\frac{x+5}{(x+6)^2}\right) \mathrm{d} x$ is

21Indefinite Integration

\(\int \frac{1}{\mathrm{e}^x+1} \mathrm{~d} x=\)

22Indefinite Integration

$\int \frac{\mathrm{d} x}{3 \cos 2 x+5}$ equals

23Indefinite Integration

$\int \frac{x^4 \cos \left(\tan ^{-1} x^5\right)}{1+x^{10}} d x$ equals

24Indefinite Integration

\(\int \frac{\mathrm{d} x}{(x+\mathrm{a})^{\frac{9}{7}}(x-\mathrm{b})^{\frac{5}{7}}}=\)

25Indefinite Integration

$\int \frac{\mathrm{d} x}{x\left(x^3+1\right)}=$

26Indefinite Integration

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

27Indefinite Integration

\(\int \frac{\mathrm{d} x}{\sqrt{x}+x}=\)

28Indefinite Integration

\(\int \frac{\mathrm{d} x}{\mathrm{e}^x-1}=\)

29Indefinite Integration

\(\int \sqrt{x^2+3 x} d x=\)

30Indefinite Integration

\(\int \frac{(5 \sin \theta-2) \cos \theta}{\left(5-\cos ^2 \theta-4 \sin \theta\right)} d \theta=\)

31Indefinite Integration

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

32Indefinite Integration

\(\int \frac{\cos 2 x-\cos 2 \alpha}{\cos x-\cos \alpha} d x=\)

33Indefinite Integration

If $\int \frac{2 x^2+3}{\left(x^2-1\right)\left(x^2-4\right)} \mathrm{d} x=\log \left[\left(\frac{x-2}{x+2}\right)^{\mathrm{a}} \cdot\left(\frac{x+1}{x-1}\right)^{\mathrm{b}}\right]+\mathrm{c}$, (where c is the constant of integration) then...

34Indefinite Integration

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

35Indefinite Integration

\(\int \mathrm{e}^{2 x} \frac{(\sin 2 x \cos 2 x-1)}{\sin ^2 2 x} \mathrm{~d} x=\)

36Indefinite Integration

\(\int \sec ^{\frac{2}{3}} x \cdot \operatorname{cosec}^{\frac{4}{3}} x d x=\)

37Indefinite Integration

\(\int \frac{x^3}{x^4+5 x^2+4} d x=\)

38Indefinite Integration

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

39Indefinite Integration

$\int \sqrt{x^2-6 x-16} \mathrm{~d} x$ equals

40Indefinite Integration

If $\quad \int \frac{3 \sin x \cos x}{4 \sin x+7} \mathrm{~d} x=\mathrm{A} \sin x-\mathrm{Blog}(4 \sin x+7)+\mathrm{c}$ where c is the constant of integration, then the value of $\mathrm{A}+\mathrm{B}$ is equal to

41Indefinite Integration

\(\int \frac{\sin x}{\sqrt{5 \sin ^2 x+6 \cos ^2 x}} d x\)

42Indefinite Integration

\(\int \cos \left(\frac{x}{16}\right) \cdot \cos \left(\frac{x}{8}\right) \cdot \cos \left(\frac{x}{4}\right) \cdot \sin \left(\frac{x}{16}\right) \mathrm{d} x=\)

43Indefinite Integration

\(\int \frac{x^3}{(x+1)^2} d x=\)

44Indefinite Integration

\(\int \sin ^5 x \mathrm{~d} x=\)

45Indefinite Integration

If $\int \frac{2 x+3}{(x-1)\left(x^2+1\right)} d x$
\(=\log _e\left\{(x-1)^{\frac{5}{2}}\left(x^2+1\right)^2\right\}-\frac{1}{2} \tan ^{-1} x+\mathrm{A}\)
where A is an arbitrary constant, then the value of $a$ is

46Indefinite Integration

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

47Indefinite Integration

\(\int \frac{\mathrm{e}^{\tan ^{-1} 2 x}}{1+4 x^2}=\)

48Indefinite Integration

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

49Indefinite Integration

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

50Indefinite Integration

\(\int \frac{\sin 2 x}{(a+b \cos x)^2} d x=\)