1
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
$$2,-7,5$$
2
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
$$\frac{x^3 \cdot \cos 3 x}{3}+\frac{x^2 \sin 3 x}{3}-\frac{2 x \cos 3 x}{9} -\frac{2 \sin 3 x}{27}+C$$
3
KCET 2019
MCQ (Single Correct Answer)
+1
-0

$$\int \frac{1}{\sqrt{x}+x \sqrt{x}} d x=$$

A
$$\tan ^{-1} \sqrt{x}+C$$
B
$$2 \log (\sqrt{x}+1)+C$$
C
$$2 \tan ^{-1} \sqrt{x}+C$$
D
$$\frac{1}{2} \tan ^{-1} \sqrt{x}+C$$
4
KCET 2019
MCQ (Single Correct Answer)
+1
-0

$$\begin{aligned} & \int \frac{2 x-1}{(x-1)(x+2)(x-3)} d x \\ & \quad=A \log |x-1|+B \log |x+2|+C \log |x-3|+K \end{aligned}$$

Then $$A, B, C$$ are respectively

A
$$\frac{1}{6}, \frac{-1}{3}, \frac{1}{3}$$
B
$$\frac{-1}{6}, \frac{1}{3}, \frac{1}{3}$$
C
$$\frac{-1}{6}, \frac{-1}{3}, \frac{1}{2}$$
D
$$\frac{1}{6}, \frac{1}{3}, \frac{1}{5}$$
KCET Subjects
EXAM MAP