Indefinite Integration · Mathematics · TS EAMCET
MCQ (Single Correct Answer)
1
$\int \frac{\sec x}{3(\sec x+\tan x)+2} d x=$
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2
$\int \frac{d x}{4+3 \cot x} d x=$
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3
$\int \frac{d x}{(x+1) \sqrt{x^{2}+4}}=$
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4
If $\int e^{x}\left(x^{3}+x^{2}-x+4\right) d x=e^{x} f(x)+c$, then $f(1)=$
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5
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 $A+B-C+D=$
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6
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)}=$
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7
If $\int\left(1+x-x^{-1}\right) e^{\left(x+x^{-1}\right)} d x=f(x)+C$, then $f(1)-f(-1)=$
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8
$ \int \frac{1}{x^{m} \sqrt[m]{x^{m}+1}} d x =$
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9
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)=$
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10
$\int \sqrt{4 \cos ^2 x-5 \sin ^2 x} \cos x d x=$
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11
$\int\left(\frac{4 \tan ^4 x+3 \tan ^2 x-1}{\tan ^2 x+4}\right) d x=$
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12
$\int\left(\frac{\left(\sin ^4 x+2 \cos ^2 x-1\right) \cos x}{(1+\sin x)^6}\right) d x=$
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13
$\int(\log x)^3 d x=$
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14
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=$
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15
$\int e^{-2 x}\left(\tan 2 x-2 \sec ^2 2 x \tan 2 x\right) d x=$
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16
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))=$
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17
$\int \frac{d x}{9 \cos ^2 2 x+16 \sin ^2 2 x}=$
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18
$\int \frac{2 \cos 3 x-3 \sin 3 x}{\cos 3 x+2 \sin 3 x} d x=$
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19
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=$
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20
$\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)= $$
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21
$\int \frac{\left(1-4 \sin ^2 x\right) \cos x}{\cos (3 x+2)} d x=$
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22
$\int \frac{\left(1-4 \sin ^2 x\right) \cos x}{\cos (3 x+2)} d x=$
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