1
VITEEE 2025
MCQ (Single Correct Answer)
+4
-1

$\int \frac{e^{x^2}\left(2 x+x^3\right)}{\left(3+x^2\right)^2} d x$ is equal to

A

$\frac{e^{x^2}}{\left(3+x^2\right)}+c$

B

$\frac{1}{4} \frac{e^{x^2}}{\left(3+x^2\right)}+c$

C

$\frac{1}{8} \frac{e^{x^2}}{\left(3+x^2\right)}+c$

D

$\frac{1}{2} \frac{e^{x^2}}{\left(3+x^2\right)}+c$

2
VITEEE 2022
MCQ (Single Correct Answer)
+4
-1

The integral $$\int \frac{d x}{x^2\left(x^4+1\right)^{3 / 4}}$$ equals

A
$$\left[\frac{x^4+1}{x^4}\right]^{1 / 4}+C$$
B
$$\left(x^4+1\right)^{1 / 4}+C$$
C
$$-\left(x^4+1\right)^{1 / 4}+C$$
D
$$-\left(\frac{x^4+1}{x^4}\right)^{1 / 4}+C$$
3
VITEEE 2021
MCQ (Single Correct Answer)
+4
-1

Evaluate $$\int \frac{3 x-2}{(x+3)(x+1)^2} d x$$.

A
$$\frac{11}{4} \log [|x+1||x+3|]+\frac{5}{2(x+1)}+C$$
B
$$\frac{11}{4} \log \left|\frac{x+3}{x+1}\right|+\frac{1}{x+1}+C$$
C
$$\frac{11}{4} \log |x+2|+\frac{5}{2}(x+3)+\frac{1}{x+1}+C$$
D
$$\frac{11}{4} \log \left|\frac{x+1}{x+3}\right|+\frac{5}{2(x+1)}+C$$

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