Indefinite Integration · Mathematics · COMEDK

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MCQ (Single Correct Answer)

1
$\int \frac{\sin x+\cos x}{\sqrt{1+2 \sin x \cos x}} d x=\varphi(x)+C$ Then $\varphi(x)=$
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2
$\int \frac{e^{\tan ^{-1} x}}{\left(1+x^2\right)}\left(1+x+x^2\right) d x=$
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3
$\int \frac{x}{(x-1)(x-2)^2} d x=a \log \left|\frac{x-1}{x-2}\right|+\frac{b}{(x-2)}+c$ then
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4
$\int \frac{d x}{x \sqrt{4 x^2-9}}=$
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5
$\int \frac{1}{\sqrt{9+8 x-x^2}} d x=\varphi(x)+c$ then $\varphi(x)=$
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6
$\int \tan ^2\left(5-\frac{x}{2}\right) d x=$
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7
$\int \log x^2 d x=$
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8
$\int \frac{d x}{(x+2)\left(x^2+1\right)}=p \log |x+2|+q \log \left|x^2+1\right|+r \tan ^{-1} x+c$ then $p+q+r=$
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9

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

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10

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

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11

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

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12

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

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13

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

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14

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

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15

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

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16

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

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17

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

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18

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

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19

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

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20

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

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21

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

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22

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

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23

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

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24

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

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25

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

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26

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

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27

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

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28

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

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29

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

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30

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

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31

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

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