1
TS EAMCET 2020 (Online) 14th September Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int \frac{d x}{(x-2) \sqrt{x^2-3 x+5}}= $$

A

$\frac{-1}{\sqrt{3}} \cosh ^{-1}\left[\frac{7 x-8}{\sqrt{37}(x-2)}\right]+C$

B

$\frac{-1}{\sqrt{3}} \sinh ^{-1}\left[\frac{x+4}{\sqrt{11}(x-2)}\right]+C$

C

$\frac{-1}{\sqrt{3}} \cosh ^{-1}\left[\frac{x+4}{\sqrt{11}(x-2)}\right]+C$

D

$\frac{-1}{\sqrt{3}} \sinh ^{-1}\left[\frac{7 x-8}{\sqrt{37}(x-2)}\right]+C$

2
TS EAMCET 2020 (Online) 14th September Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $5(f(x))^2=x f(x)+30$ and

$$ \begin{aligned} & \int \frac{\left(3 x^3+\left(1-30 x^2\right) f(x)\right)}{(10 f(x)-x)\left(x^3-f(x)\right)^2} d x \\ & =\frac{A}{B x^3+D f(x)}+C \text { then } A+B+D= \end{aligned} $$

A

2

B

1

C

$\frac{1}{2}$

D

-1

3
TS EAMCET 2020 (Online) 14th September Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $\int x[\log (1+x)]^3 d x=\frac{(1+x)^2}{16}(f(x))+(1+x)(g(x))$, then

$$ f(x)+g(x)= $$

A

$\log (1+x)\left[6+9(\log (1+x))-7(\log (1+x))^2\right]+C$

B

$\log (1+x) x^3+7(\log (1+x))^2+4 \log (1+x)+C$

C

$12-18 \log (1+x)+15(\log (1+x))^2-9(\log (1+x))^3+C$

D

$6 \log (1+x)-9(\log (1+x))^2+7(\log (1+x))^3+C$

4
TS EAMCET 2020 (Online) 14th September Morning Shift
MCQ (Single Correct Answer)
+1
-0

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

A

$\frac{x}{\sqrt{1+x^2}}+C$

B

$\log \left|x+\sqrt{1+x^2}\right|+C$

C

$x+\sqrt{1+x^2}+C$

D

$\frac{\left(x+\sqrt{1+x^2}\right)^2}{2}+C$

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