1
AP EAPCET 2022 - 4th July Morning Shift
+1
-0

If $$I_n=\int \tan ^n x d x$$, and $$I_0+I_1+2 I_2+2 I_3+2 I_4 +I_5+I_6=\sum_\limits{k=1}^n \frac{\tan ^k x}{k}$$, then $$n=$$

A
6
B
5
C
4
D
3
2
AP EAPCET 2022 - 4th July Morning Shift
+1
-0

$$\int \frac{e^{\cot x}}{\sin ^2 x}(2 \log \operatorname{cosec} x+\sin 2 x) d x=$$

A
$$-2 e^{\cot x} \log \left(\operatorname{cosec}^2 x\right)+C$$
B
$$-2 e^{\cot x} \log (\operatorname{cosec} x)+C$$
C
$$-2 e^{\cot x} \log (\operatorname{cosec} x+\sin x)+C$$
D
$$-2 e^{\cot x} \log (\operatorname{cosec} x-\cot x)+C$$
3
AP EAPCET 2022 - 4th July Morning Shift
+1
-0

The parametric form of a curve is $$x=\frac{t^3}{t^2-1} y=\frac{t}{t^2-1}$$, then $$\int \frac{d x}{x-3 y}=$$

A
$$\frac{1}{2} \log \left(t^2-1\right)+C$$
B
$$2 \log \left(t\left(t^2-1\right)\right)+C$$
C
$$\frac{1}{4} \log \left(\frac{t}{t^2-3}\right)+C$$
D
$$\frac{5}{2} \log \left(t+\frac{1}{t^2}\right)+C$$
4
AP EAPCET 2021 - 20th August Morning Shift
+1
-0

Given, $$\frac{3 x-2}{(x+1)^2(x+3)}=\frac{A}{x+1} +\frac{B}{(x+1)^2}+\frac{C}{x+3}$$, then $$4 A+2 B+4 C$$ is equal to

A
5
B
$$-$$5
C
$$-$$3
D
3
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