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

If $$\int \frac{1-(\cot x)^{2021}}{\tan x+(\cot x)^{2022}} d x=\frac{1}{A} \log\left|(\sin x)^{2023}+(\cos x)^{2023}\right|+c$$, then $$A$$ is equal to

A
2020
B
2021
C
2022
D
2023
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