1
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
$$\sqrt{e^{4 x}+e^{2 x}}+\sqrt{e^{2 x}+1}+c$$
2
AP EAPCET 2021 - 19th August Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $$\int \frac{1}{1+\sin x} d x=\tan (f(x))+c$$, then $$f^{\prime}(0)$$ is equal to

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

$$\int \frac{e^x(x+3)}{(x+5)^3} d x$$ is equal to

A
$$\frac{e^x}{(x+5)^2}+C$$
B
$$e^x(x+5)^2+C$$
C
$$e^x(x+3)^2+C$$
D
$$\frac{e^x}{(x+3)^2}+C$$
4
AP EAPCET 2021 - 19th August Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $$\int \frac{(x-1)^2}{\left(x^2+1\right)^2} d x=\tan ^{-1}(x)+g(x)+k$$, then $$g(x)$$ is equal to

A
$$\tan ^{-1}\left(\frac{x}{2}\right)$$
B
$$\frac{1}{x^2+1}$$
C
$$\frac{1}{2\left(x^2+1\right)}$$
D
$$\frac{2}{x^2+1}$$
AP EAPCET Subjects
EXAM MAP