55
MCQ (Single Correct Answer)
If $\frac{x^3 d x}{\sqrt{1+x^2}}=a\left(1+x^2\right)^{3 / 2}+b \sqrt{1+x^2}+C$, then
A
$a=\frac{1}{3}, b=1$
B
$a=\frac{-1}{3}, b=1$
C
$a=\frac{-1}{3}, b=-1$
D
$a=\frac{1}{3}, b=-1$
56
MCQ (Single Correct Answer)
$\int_{-\pi / 4}^{\pi / 4} \frac{d x}{1+\cos 2 x}$ is equal to
A
1
B
2
C
3
D
4
57
MCQ (Single Correct Answer)
$\int_0^{\pi / 2} \sqrt{1-\sin 2 x} d x$ is equal to
A
$2 \sqrt{2}$
B
$2(\sqrt{2}+1)$
C
$2$
D
$2(\sqrt{2}-1)$
58
MCQ (Single Correct Answer)
$\int_0^{\pi / 4} \cos x e^{\sin x} d x$ is equal to
A
$e+1$
B
$e-1$
C
$e$
D
$-e$
59
MCQ (Single Correct Answer)
$\int \frac{x+3}{(x+4)^2} e^x d x$ is equal to
A
$\mathrm{e}^x\left(\frac{1}{x+4}\right)+C$
B
$\mathrm{e}^{-x}\left(\frac{1}{x+4}\right)+C$
C
$\mathrm{e}^{-x}\left(\frac{1}{x-4}\right)+C$
D
$\mathrm{e}^{2 x}\left(\frac{1}{x-4}\right)+C$