1
KCET 2021
+1
-0

$$\int \frac{x^3 \sin \left(\tan ^{-1}\left(x^4\right)\right)}{1+x^8} d x$$ is equal to

A
$$\frac{-\cos \left(\tan ^{-1}\left(x^4\right)\right)}{4}+C$$
B
$$\frac{\cos \left(\tan ^{-1}\left(x^4\right)\right)}{4}+C$$
C
$$\frac{-\cos \left(\tan ^{-1}\left(x^3\right)\right)}{3}+C$$
D
$$\frac{\sin \left(\tan ^{-1}\left(x^4\right)\right)}{4}+C$$
2
KCET 2021
+1
-0

The value of $$\int \frac{x^2 d x}{\sqrt{x^6+a^6}}$$ is equal to

A
$$\log \left|x^3+\sqrt{x^6+a^6}\right|+C$$
B
$$\log \left|x^3-\sqrt{x^6+a^6}\right|+C$$
C
$$\frac{1}{3} \log \left|x^3+\sqrt{x^6+a^6}\right|+C$$
D
$$\frac{1}{3} \log \left|x^3-\sqrt{x^6+a^6}\right|+C$$
3
KCET 2021
+1
-0

The value of $$\int \frac{x e^x d x}{(1+x)^2}$$ is equal to

A
$$e^x(1+x)+C$$
B
$$e^x\left(1+x^2\right)+C$$
C
$$e^x(1+x)^2+C$$
D
$$\frac{e^x}{1+x}+C$$
4
KCET 2021
+1
-0

The value of $$\int e^x\left[\frac{1+\sin x}{1+\cos x}\right] d x$$ is equal to

A
$$e^x \tan \frac{x}{2}+C$$
B
$$e^x \tan x+C$$
C
$$e^x(1+\cos x)+C$$
D
$$e^x(1+\sin x)+C$$
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