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1
KCET 2020
MCQ (Single Correct Answer)
+1
-0

The value of $$\int \frac{1+x^4}{1+x^6} d x$$ is

A
$$\tan ^{-1} x+\tan ^{-1} x^3+C$$
B
$$\tan ^{-1} x+\frac{1}{3} \tan ^{-1} x^3+C$$
C
$$\tan ^{-1} x-\frac{1}{3} \tan ^{-1} x^3+C$$
D
$$\tan ^{-1} x+\frac{1}{3} \tan ^{-1} x^2+C$$
2
KCET 2020
MCQ (Single Correct Answer)
+1
-0

The value of $$\int e^{\sin x} \sin 2 x d x$$ is

A
$$2 e^{\sin x}(\sin x-1)+C$$
B
$$2 e^{\sin x}(\sin x+1)+C$$
C
$$2 e^{\sin x}(\cos x+1)+C$$
D
$$2 e^{\sin x}(\cos x-1)+C$$
3
KCET 2020
MCQ (Single Correct Answer)
+1
-0

If $$\int \frac{3 x+1}{(x-1)(x-2)(x-3)} d x A \log |x-1| B \log |x-2|+C \log |x-3|+C$$, then the values of $$A, B$$ and $$C$$ are respectively

A
$$5,-7,-5$$
B
$$2,-7,-5$$
C
$$5,-7,5$$
D
$$2,-7,5$$
4
KCET 2019
MCQ (Single Correct Answer)
+1
-0

$$\int x^3 \sin 3 x d x=$$

A
$$-\frac{x^3 \cdot \cos 3 x}{3}+\frac{x^2 \sin 3 x}{3}+\frac{2 x \cos 3 x}{9} -\frac{2 \sin 3 x}{27}+C$$
B
$$-\frac{x^3 \cdot \cos 3 x}{3}-\frac{x^2 \sin 3 x}{3}+\frac{2 x \cos 3 x}{9} -\frac{2 \sin 3 x}{27}+C$$
C
$$-\frac{x^3 \cdot \cos 3 x}{3}+\frac{x^2 \sin 3 x}{3}-\frac{2 x \cos 3 x}{9} -\frac{2 \sin 3 x}{27}+C$$
D
$$\frac{x^3 \cdot \cos 3 x}{3}+\frac{x^2 \sin 3 x}{3}-\frac{2 x \cos 3 x}{9} -\frac{2 \sin 3 x}{27}+C$$
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