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1
AP EAPCET 2021 - 19th August Evening Shift
MCQ (Single Correct Answer)
+1
-0

Which of the following is partial fraction of $$\frac{-x^2+6 x+13}{(3 x+5)\left(x^2+4 x+4\right)}$$ is equal to

A
$$\frac{3}{3 x+5}+\frac{-1}{x+2}+\frac{2}{(x+2)^2}$$
B
$$\frac{2}{3 x+5}+\frac{-1}{x+2}+\frac{3}{(x+2)^2}$$
C
$$\frac{-1}{3 x+5}+\frac{2}{x+2}+\frac{3}{(x+2)^2}$$
D
$$\frac{3}{3 x+5}+\frac{2}{x+2}+\frac{-1}{(x+2)^2}$$
2
AP EAPCET 2021 - 19th August Evening Shift
MCQ (Single Correct Answer)
+1
-0

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

A
$$\frac{1}{2}(\sqrt{1+x})+c$$
B
$$\sqrt{1+x}+c$$
C
$$2(1+x)^{3 / 2}+c$$
D
$$\frac{2}{3}(1+x)^{3 / 2}+c$$
3
AP EAPCET 2021 - 19th August Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$\int(\cos x) \log \cot \left(\frac{x}{2}\right) d x$$ is equal to

A
$$(\sin x) \log \cot \left(\frac{x}{2}\right)+c$$
B
$$(\cos x) \log \cot \left(\frac{x}{2}\right)+c$$
C
$$(\sin x) \log \cot \left(\frac{x}{2}\right)+x+c$$
D
$$(\sin x) \log \cot \left(\frac{x}{2}\right)-x+c$$
4
AP EAPCET 2021 - 19th August Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$\int \sqrt{e^{4 x}+e^{2 x}} d x$$ is equal to

A
$$\frac{1}{2} e^x\left(\sqrt{e^{2 x}+1}\right)+\frac{1}{2} \sinh ^{-1}\left(e^x\right)+c$$
B
$$\frac{1}{2} e^x\left(\sqrt{e^{2 x}+1}\right)+\sinh ^{-1}\left(e^x\right)+c$$
C
$$\frac{1}{2}\left(\sqrt{e^{2 x}+1}\right)+\frac{1}{2} \sinh ^{-1}\left(e^x\right)+c$$
D
$$\sqrt{e^{4 x}+e^{2 x}}+\sqrt{e^{2 x}+1}+c$$
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