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

If $\int\left(3 t^2 \sin \frac{1}{t}-t \cos \frac{1}{t}\right) d t=f(t) \sin \left(\frac{1}{t}\right)+C$ then $f(2)=$

A

2

B

-12

C

8

D

-16

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

$$ \int(\log x)^3 x^4 d x= $$

A
$x^5\left[\frac{1}{5}(\log x)^3-\frac{3}{25}(\log x)^2+\frac{6}{125} \log x-\frac{6}{625}\right]+C$
B
$x^5\left[\frac{1}{5}(\log x)^3-\frac{2}{25}(\log x)^2+\frac{6}{125} \log x-\frac{12}{125}\right]+C$
C

$x^5\left[\frac{1}{5}(\log x)^3-\frac{4}{25}(\log x)^2-\frac{9}{125} \log x-\frac{8}{125}\right]+C$

D

$x^5\left[\frac{1}{5}(\log x)^3+\frac{3}{25}(\log x)^2-\frac{6}{125} \log x-\frac{6}{125}\right]+C$

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

$$ \int \frac{\sin 2 x}{\sin ^2 x+3 \cos x-3} d x $$

A

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

B

$\log \left(\frac{(\cos x-2)^2}{(\cos x-1)^4}\right)+C$

C

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

D

$\log \left(\frac{(\cos x-2)^4}{(\cos x-1)^2}\right)+C$

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

If $\int \frac{d x}{\sin ^3 x+\cos ^3 x}=A \log \left|\frac{\sqrt{2}+t}{\sqrt{2}-t}\right|+B \tan ^{-1}(t)+C$, then $\left(\frac{B}{A}, t\right)=$

A

$(3 \sqrt{2}, \sin x-\cos x)$

B

$(2 \sqrt{2}, \sin x-\cos x)$

C

$\left(\frac{\sqrt{2}}{3}, \sin x-\cos x\right)$

D

$\left(\frac{3}{\sqrt{2}}, \sin x+\cos x\right)$

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