\(\int \sqrt{\frac{1-x}{1+x}} d x\) is

(a)

\(\sqrt{1-x^2}+sin^{-1}x+c\)

(b)

\(sin^{-1}x-\sqrt{1-x^2}+c\)

(c)

\(log|x+\sqrt{1-x^2}|-\sqrt{1-x^2}+c\)

(d)

\(\sqrt{1-x^2}+log|x+\sqrt{1-x^2}|+c\)

\(\int \frac{d x}{e^x-1}\) is

(a)

\(log|e^x|-log|e^x-1|+c\)

(b)

\(log|e^x|+log|e^x-1|+c\)

(c)

\(log|e^x-1|-log|e^x|+c\)

(d)

\(log|e^x+1|-log|e^x|+c\)

\(\int e^{-4 x} \cos x d x\) is

(a)

\({e^{-4x}\over 17}[4cos \ x-sin \ x]+c\)

(b)

\({e^{-4x}\over 17}[-4cos \ x+sin \ x]+c\)

(c)

\({e^{-4x}\over 17}[4cos \ x+sin \ x]+c\)

(d)

\({e^{-4x}\over 17}[-4cos \ x-sin \ x]+c\)

\(\int \frac{\sec ^2 x}{\tan ^2 x-1} d x\) is

(a)

\(2log|{1-tan x\over 1+tan \ x}|+c\)

(b)

\(log|{1+tan x\over 1-tan \ x}|+c\)

(c)

\({1\over2}log|{tan x+1\over tan \ x-1}|+c\)

(d)

\({1\over2}log|{tan x-1\over tan \ x+1}|+c\)

\(\int e^{-7 x} \sin 5 x d x\) is

(a)

\({e^{-7x}\over 74}[-7sin 5x-5cos 5x]+c\)

(b)

\({e^{-7x}\over 74}[7sin 5x+5cos 5x]+c\)

(c)

\({e^{-7x}\over 74}[7sin 5x-5cos 5x]+c\)

(d)

\({e^{-7x}\over 74}[-7sin 5x+5cos 5x]+c\)

\(\int x^2 e^{\frac{x}{2}} d x\) is

(a)

\( x^2e^{x\over2}-4xe^{x\over2}-8e^{x\over2}+c\)

(b)

\( 2x^2e^{x\over2}-8xe^{x\over2}-16e^{x\over2}+c\)

(c)

\( 2x^2e^{x\over2}-8xe^{x\over2}+16e^{x\over2}+c\)

(d)

\( x^2{e^{x\over2}\over 2}-{xe^{x\over2}\over 4}+{e^{x\over2}\over 8}+c\)

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

(a)

\(\sqrt{x^2-1}-2 log|x+\sqrt{x^2-1}|+c\)

(b)

\(sin^{-1}x-2 log|x+\sqrt{x^2-1}|+c\)

(c)

\(2 log|x+\sqrt{x^2-1}|-sin^{-1}x+c\)

(d)

\(\sqrt{x^2-1}+2log|x+\sqrt{x^2-1}|+c\)

\(\int \frac{1}{x \sqrt{(\log x)^2-5}} d x\) is

(a)

\(log|x+\sqrt{x^2-5}|+c\)

(b)

\(log|logx+\sqrt{logx-5}|+c\)

(c)

\(log|logx+\sqrt{(logx)^2-5}|+c\)

(d)

\(log|logx-\sqrt{(logx)^2-5}|+c\)

\(\int \sin \sqrt{x} d x\) is

(a)

\(2(-\sqrt{x}cos\sqrt{x}+sin\sqrt{x})+c\)

(b)

\(2(-\sqrt{x}cos\sqrt{x}-sin\sqrt{x})+c\)

(c)

\(2(-\sqrt{x}sin\sqrt{x}-cos\sqrt{x})+c\)

(d)

\(2(-\sqrt{x}sin\sqrt{x}+cos\sqrt{x})+c\)

\(\int e^{\sqrt{x}} d x\) is

(a)

\(2\sqrt{x}(1-e^{\sqrt{x}})+c\)

(b)

\(2\sqrt{x}(e^{\sqrt{x}}-1)+c\)

(c)

\(2e^{\sqrt{x}}(1-\sqrt{x})+c\)

(d)

\(2e^{\sqrt{x}}(\sqrt{x}-1)+c\)