Indefinite Integration PYQs - Last 5 Years

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All Indefinite Integration PYQs Last 10 Years Create chapter test

Practice 104 TS EAMCET 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 104 filtered questions.

1Indefinite Integration

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

2Indefinite Integration

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

3Indefinite Integration

If $I_1=\int \sin ^6 x d x$ and $I_2=\int \cos ^6 x d x$, then $I_1+I_2=$

4Indefinite Integration

If $\int x^3 \sin 3 x d x=\frac{1}{27}[f(x) \cos 3 x+g(x) \sin 3 x]+C$, then $f(\mathrm{l})+g(\mathrm{l})=$

5Indefinite Integration

$$ \begin{aligned} &\text { If } y=f(x)^{g(x)} \text { and } \frac{d y}{d x}=y\left[H(x) f^{\prime}(x)+G(x) g^{\prime}(x)\right] \text {, then }\\ &\int \frac{G(x) H(x) f^{\prime}(x)}{g(x)} d x= \end{aligned} $$

6Indefinite Integration

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

7Indefinite Integration

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

8Indefinite Integration

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

9Indefinite Integration

$$ \begin{aligned} I_1 & =\int \frac{e^x}{e^{4 x}+e^{2 x}+1} d x, I_2 \\ & =\int \frac{e^{-x}}{e^{-4 x}+e^{-2 x}+1} d x, \text { then } I_2-I_1= \end{aligned} $$

10Indefinite Integration

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

11Indefinite Integration

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

12Indefinite Integration

\(\int\left(1+\tan ^2 x\right)(1+2 x \tan x) d x=\)

13Indefinite Integration

\(\int e^{-x}\left(x^3-2 x^2+3 x-4\right) d x=\)

14Indefinite Integration

If $\frac{x+3}{(x+1)\left(x^2+2\right)}=\frac{a}{x+1}+\frac{b x+c}{x^2+2}$, then $a-b+c=$

15Indefinite Integration

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

16Indefinite Integration

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

17Indefinite Integration

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

18Indefinite Integration

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

19Indefinite Integration

If $\frac{5 \pi}{4} < x < \frac{7 \pi}{4}$, then $\int \sqrt{\frac{1-\sin 2 x}{1+\sin 2 x}} d x=$

20Indefinite Integration

If $\int(x+2) \sqrt{x^2-x+2} d x=\frac{1}{3} f(x)+\frac{5}{8} g(x)+\frac{35}{16} h(x)+C$ then $f(-1)+g(-1)+h\left(\frac{1}{2}\right)=$

21Indefinite Integration

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

22Indefinite Integration

\(\int e^{4 x}(\sin 3 x-\cos 3 x) d x=\)

23Indefinite Integration

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

24Indefinite Integration

If $\int \frac{d x}{\left(x^2+9\right) \sqrt{x^2+16}}=\frac{1}{3 \sqrt{7}} \tan ^{-1}\left(K \frac{x}{\sqrt{16+x^2}}\right)+c$, then $K=$

25Indefinite Integration

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

26Indefinite Integration

\(\int\left(\frac{1}{x^2}+\frac{\sin ^3 x+\cos ^3 x}{\sin ^2 x \cos ^2 x}\right) d x=\)

27Indefinite Integration

If $I_n=\int \frac{1}{\left(x^2+1\right)^n} d x$, then $2 n I_{n+1}-(2 n-1) I_n=$

28Indefinite Integration

$\int \frac{x^3}{x^4+3 x^2+2} d x=$

29Indefinite Integration

$\int \frac{1}{x^{m \sqrt[m]{m}} x^{m}+1} d x=$

30Indefinite Integration

$\int \frac{\left(1-4 \sin ^2 x\right) \cos x}{\cos (3 x+2)} d x=$

31Indefinite Integration

$\int(\sqrt{1-\sin x}+\sqrt{1+\sin x}) d x=f(x)+c$, where $c$ is the constant of integration. If $\frac{5 \pi}{2}$<$x<\frac{7 \pi}{2}$ and \(f\left(\frac{8 \pi}{3}\right)=-2, \text { then } f^{\prime}\left(\frac{8 \pi}{3}\right)=\)

32Indefinite Integration

$\int \frac{\left(1-4 \sin ^2 x\right) \cos x}{\cos (3 x+2)} d x=$

33Indefinite Integration

If $\frac{x^4}{\left(x^2+1\right)(x-2)}=f(x)+\frac{A x+B}{x^2+1}+\frac{C}{x-2}$, then $f(14)+2 A-B=$

34Indefinite Integration

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

35Indefinite Integration

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

36Indefinite Integration

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

37Indefinite Integration

$\int \frac{d x}{9 \cos ^2 2 x+16 \sin ^2 2 x}=$

38Indefinite Integration

If $\int x^3 \sin 3 x d x=f(x) \cos 3 x+g(x) \sin 3 x+C$, then 27 $(f(x)+x g(x))=$

39Indefinite Integration

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

40Indefinite Integration

$\int \frac{\sec x}{3(\sec x+\tan x)+2} d x=$

41Indefinite Integration

If $\int e^{x}\left(x^{3}+x^{2}-x+4\right) d x=e^{x} f(x)+c$, then $f(1)=$

42Indefinite Integration

$\int \frac{d x}{4+3 \cot x} d x=$

43Indefinite Integration

$\int\left(\frac{\left(\sin ^4 x+2 \cos ^2 x-1\right) \cos x}{(1+\sin x)^6}\right) d x=$

44Indefinite Integration

$\int\left(\frac{4 \tan ^4 x+3 \tan ^2 x-1}{\tan ^2 x+4}\right) d x=$

45Indefinite Integration

$\int \sqrt{4 \cos ^2 x-5 \sin ^2 x} \cos x d x=$

46Indefinite Integration

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

47Indefinite Integration

If $\int \frac{1}{x^{4}+8 x^{2}+9} d x=\frac{1}{k}$$\left[\frac{1}{\sqrt{14}} \tan ^{-1}(f(x))-\frac{1}{\sqrt{2}} \tan ^{-1}(g(x))\right]+c$ then,$\sqrt{\frac{k}{2}+f(\sqrt{3})+g(1)}=$

48Indefinite Integration

$ \int \frac{1}{x^{m} \sqrt[m]{x^{m}+1}} d x =$

49Indefinite Integration

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

50Indefinite Integration

If $\int(\sqrt{\operatorname{cosec} x+1}) d x=k \tan ^{-1}(f(x))+C$, then $\frac{1}{k} f\left(\frac{\pi}{6}\right)=$