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

If $$f(x)=\int x^2 \cos ^2 x\left(2 x \tan ^2 x-2 x-6 \tan x\right) d x$$ and $$f(0)=\pi$$, then $$f(x)=$$

A
$$x^2 \sin x+\pi$$
B
$$\cos x+\pi-1$$
C
$$-x^3 \sin 2 x+\pi$$
D
$$x^3 \cos 2 x+\pi \cos x$$
2
AP EAPCET 2022 - 4th July Evening Shift
+1
-0

If $$\int \frac{e^{\sqrt{x}}}{\sqrt{x}}(x+\sqrt{x}) d x=e^{\sqrt{x}}[A x+B \sqrt{x}+C]+K$$ then $$A+B+C=$$

A
$$-$$2
B
2
C
4
D
$$-$$4
3
AP EAPCET 2022 - 4th July Evening Shift
+1
-0

If $$\int \frac{1+\sqrt{\tan x}}{\sin 2 x} d x=A \log \tan x+B \tan x+C$$, then $$4 A-2 B=$$

A
$$-$$1
B
2
C
1
D
$$-$$2
4
AP EAPCET 2022 - 4th July Evening Shift
+1
-0

$$\int \frac{1+\tan x \tan (x+a)}{\tan x \tan (x+a)} d x=$$

A
$$\tan a(\log (\sec (x+a))+\log \sec x+C$$
B
$$\cot a(\log |\sin x|-\log |\sin (x+a)|)+C$$
C
$$\tan a\left(\log \left(\frac{\cos x}{\sin (x+a)}\right)\right)+C$$
D
$$\cot a\left(\log \frac{\sin (x+a)}{\cos (x+a)}\right)+C$$
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