Indefinite Integration PYQs - Last 5 Years

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All Indefinite Integration PYQs Last 10 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.

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Last 5 Years Indefinite Integration Questions

Showing 50 of 147 filtered questions.

1Indefinite Integration

If $\int e^{\sin x}(1+\sec x \tan x) d x=e^{\sin x} f(x)+c$, then in $0 \leq x \leq 2 \pi$, then number of solutions of $f(x)=1$ is

2Indefinite Integration

If $\int \frac{d x}{(x-1)^{\frac{3}{2}}(x-3)^{\frac{1}{2}}}=\sqrt{f(x)}+C$, then $f(-1)-f(0)=$

3Indefinite Integration

If $\int\left(3 t^2 \sin \frac{1}{t}-t \cos \frac{1}{t}\right) d t=f(t) \sin \left(\frac{1}{t}\right)+C$ then $f(2)=$

4Indefinite Integration

\(\int(\log x)^3 x^4 d x=\)

5Indefinite Integration

\(\int \frac{e^{\sin x}(\sin 2 x-8 \cos x)}{2(\sin x-3)^2} d x=\)

6Indefinite Integration

If $\int \frac{d x}{\sin ^3 x+\cos ^3 x}=A \log \left|\frac{\sqrt{2}+t}{\sqrt{2}-t}\right|+B \tan ^{-1}(t)+C$, then $\left(\frac{B}{A}, t\right)=$

7Indefinite Integration

\(\int \frac{\sin 2 x}{\sin ^2 x+3 \cos x-3} d x\)

8Indefinite Integration

If $\int \frac{\sin x \cos x}{\sqrt{\cos ^4 x-\sin ^4 x}} d x=-\frac{f(x)}{2}+c$, then domain of $f(x)$ is

9Indefinite Integration

If $\int \frac{\sqrt[4]{x}}{\sqrt{x}+\sqrt[4]{x}} d x=$ $\frac{2}{3}\left[A \sqrt[4]{x^3}+B \sqrt[4]{x^2}+C \sqrt[4]{x}+D \log (1+\sqrt[4]{x})\right]+K$, then $\frac{2}{3}(A+B+C+D)$ is equal to

10Indefinite Integration

$\int \sin ^{-1}\left(\sqrt{\frac{x-a}{x}}\right) d x$ is equal to

11Indefinite Integration

$\frac{4 x^2+5}{(x-2)^4}=\frac{A}{(x-2)}+\frac{B}{(x-2)^2}+\frac{C}{(x-2)^3}+\frac{D}{(x-2)^4}$, then $\sqrt{\frac{A}{C}+\frac{B}{C}+\frac{D}{C}}$ is equal to

12Indefinite Integration

$\int(\log x)^m x^n d x$ is equal to

13Indefinite Integration

\(\int \frac{\sin 7 x}{\sin 2 x \sin 5 x} d x=\)

14Indefinite Integration

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

15Indefinite Integration

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

16Indefinite Integration

\(\int \frac{x^3 \tan ^{-1} x^4}{1+x^8} d x=\)

17Indefinite Integration

\(\int \frac{x^2-1}{x^3 \sqrt{2 x^4-2 x^2+1}} d x\)

18Indefinite Integration

If $\int \log \left(6 \sin ^2 x+17 \sin x+12\right) \cos x d x=f(x)+c$, then $f\left(\frac{\pi}{2}\right)$ is equal to

19Indefinite Integration

$\int \sin ^4 x \cos ^4 x d x$ is equal to

20Indefinite Integration

\(\text { If } \frac{13 x+43}{2 x^2+17 x+30}=\frac{A}{2 x+5}+\frac{B}{x+6} \text {, then } A+B \text { is equal to }\)

21Indefinite Integration

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

22Indefinite Integration

$\int\left[(\log 2 x)^2+2 \log 2 x\right] d x$ is equal to

23Indefinite Integration

$\int e^{4 x^2+8 x-4}(x+1) \cos \left(3 x^2+6 x-4\right) d x$ is equal to

24Indefinite Integration

If $x \in\left[2 n \pi-\frac{\pi}{4}, 2 n \pi+\frac{3 \pi}{4}\right]$ and $n \in Z$, then $\int \sqrt{1-\sin 2 x} d x=$

25Indefinite Integration

If $\int \frac{1}{1-\cos x} d x=\tan \left(\frac{x}{\alpha}+\beta\right)+c$, then one of the values of $\frac{\pi \alpha}{4}-\beta$ is

26Indefinite Integration

If $n \geq 2$ is a natural number and $0<\theta<\frac{\pi}{2}$, then $\int \frac{\left(\cos ^n \theta-\cos \theta\right)^{1 / n}}{\cos ^{n+1} \theta} \sin \theta d \theta=$

27Indefinite Integration

If $\frac{1}{(3 x+1)(x-2)}=\frac{A}{3 x+1}+\frac{B}{x-2}$ and $\frac{x+1}{(3 x+1)(x-2)}=\frac{C}{3 x+1}+\frac{D}{x-2}$, then

28Indefinite Integration

$\int e^x\left(\frac{x+2}{x+4}\right)^2 d x=$

29Indefinite Integration

If $\frac{x+2}{\left(x^2+3\right)\left(x^4+x^2\right)\left(x^2+2\right)}=\frac{A x+B}{x^2+3}+\frac{C x+D}{x^2+2}$ $+\frac{E x^3+F x^2+G x+H}{x^4+x^2}$, then $(E+F)(C+D)(A)=$

30Indefinite Integration

$\int \frac{x^5}{x^2+1} d x=$

31Indefinite Integration

$\int \frac{\sin ^6 x}{\cos ^8 x} d x=$

32Indefinite Integration

$\int e^x(x+1)^2 d x=$

33Indefinite Integration

$\int \frac{x^4+1}{x^6+1} d x=$

34Indefinite Integration

\(\int {\left( {\sum\limits_{r = 0}^\infty {{{{x^r}{3^r}} \over {r!}}} } \right)dx = }\)

35Indefinite Integration

$\int \frac{2 x^2-3}{\left(x^2-4\right)\left(x^2+1\right)} d x=A \tan ^{-1} x+B \log (x-2)+C \log (x+2)$, then $6 A+7 B-5 C=$

36Indefinite Integration

$$ \begin{aligned} &\text { If } \int \frac{3}{2 \cos ^3 x \sqrt{2 \sin 2 x}} d x=\frac{3}{2}(\tan x)^B+\frac{3}{10}(\tan x)^A+C \text {, than }\\&A= \end{aligned} $$

37Indefinite Integration

$\int \frac{3 x^9+7 x^8}{\left(x^2+2 x+5 x^8\right)^2} d x=$

38Indefinite Integration

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

39Indefinite Integration

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

40Indefinite Integration

If $\int \sqrt{\frac{2}{1+\sin x}} d x=2 \log |A(x)-B(x)|+C$ and $0 \leq x \leq \frac{\pi}{2}$, then $B\left(\frac{\pi}{4}\right)=$

41Indefinite Integration

$\int \frac{e^{2 x}}{\sqrt[4]{e^x+1}} d x=$

42Indefinite Integration

$\int \frac{2-\sin x}{2 \cos x+3} d x=$

43Indefinite Integration

$\int \frac{d x}{\sqrt{\sin ^3 x \cos (x-a)}}=$

44Indefinite Integration

$\int \sin ^{-1} \sqrt{\frac{x}{a+x}} d x=$

45Indefinite Integration

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

46Indefinite Integration

If $\frac{x^2+3}{x^4+2 x^2+9}=\frac{A x+B}{x^2+a x+b}+\frac{C x+D}{x^2+c x+b}$, then $a A+b B+c C+D=$

47Indefinite Integration

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

48Indefinite Integration

Let $f(x)=\int \frac{x}{\left(x^2+1\right)\left(x^2+3\right)} d x$. If $f(3)=\frac{1}{4} \log \left(\frac{5}{6}\right)$, then $f(0)=$

49Indefinite Integration

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

50Indefinite Integration

If $\frac{1}{x^4+1}=\frac{A x+B}{x^2+\sqrt{2} x+1}+\frac{C x+D}{x^2-\sqrt{2} x+1}$, then $B D-A C=$