1
AP EAPCET 2025 - 21st May Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int \frac{x}{\left(1-x^2\right) \sqrt{2-x^2}} d x= $$

A

$\log \left|\frac{\sqrt{2-x^2}+1}{\sqrt{2-x^2}-1}\right|+C$

B

$\frac{1}{2} \log \left|\frac{\sqrt{2-x^2}}{1-x^2}\right|+C$

C

$\frac{1}{2} \log \left|\frac{1+\sqrt{2-x^2}}{1-\sqrt{2-x^2}}\right|+C$

D

$\log \left|\frac{1-x^2}{\sqrt{2-x^2}}\right|+C$

2
AP EAPCET 2025 - 21st May Evening Shift
MCQ (Single Correct Answer)
+1
-0

$\int\left(\frac{1+x+\sqrt{x+x^2}}{\sqrt{x}+\sqrt{1+x}}\right) d x=$

A

$\frac{1}{2} \sqrt{1+x}+C$

B

$\frac{2}{3}(1+x)^{\frac{3}{2}}+C$

C

$\sqrt{1+x}+C$

D

$2(1+x)^{\frac{3}{2}}+C$

3
AP EAPCET 2025 - 21st May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $\int x^2 \cos ^2 x d x=\frac{1}{6} f(x)+g(x) \sin 2 x +h(x) \cos 2 x+c$, then $f(1)+g(2)+h\left(\frac{1}{2}\right)=$

A

0

B

2

C

1

D

-1

4
AP EAPCET 2025 - 21st May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int \frac{e^{\sin x}(\sin 2 x-8 \cos x)}{2(\sin x-3)^2} d x= $$

A

$e^{\sin x}(\sin x-3)+C$

B

$\frac{e^{\sin x}}{(\sin x-3)^2}+C$

C

$e^{\sin x}(\sin x-3)^2+C$

D

$\frac{e^{\sin x}}{\sin x-3}+C$

AP EAPCET Subjects

Browse all chapters by subject