1
AP EAPCET 2024 - 20th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$\int \frac{e^{2 x}}{\sqrt[4]{e^x+1}} d x=$
A
$\frac{4}{7}\left(e^x+1\right)^{\frac{4}{3}}\left(3 e^x-1\right)+c$
B
$\frac{2}{21}\left(e^x+1\right)^{\frac{3}{4}}\left(3 e^x-7\right)+c$
C
$\frac{4}{21}\left(e^x+1\right)^{3 / 4}\left(3 e^x-4\right)+c$
D
$\frac{8}{21}\left(e^x+1\right)^{3 / 4}\left(3 e^x-1\right)+c$
2
AP EAPCET 2024 - 20th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$\int \frac{2-\sin x}{2 \cos x+3} d x=$
A
$\frac{2}{\sqrt{5}} \tan ^{-1}\left(\frac{1}{\sqrt{3}} \tan \frac{x}{2}\right)-\log \sqrt{2 \cos x+3}+c$
B
$\frac{4}{\sqrt{5}} \tan ^{-1}\left(\frac{1}{\sqrt{5}} \tan \frac{x}{2}\right)+\log \sqrt{2 \cos x+3}+c$
C
$\frac{3}{\sqrt{5}} \tan ^{-1}\left(\frac{1}{\sqrt{5}} \tan \frac{x}{2}\right)+\log \sqrt{2 \cos x-3}+c$
D
$\frac{1}{\sqrt{5}} \tan ^{-1}\left(\frac{1}{\sqrt{5}} \tan \frac{x}{3}\right)-\log \sqrt{2 \cos x-3}+c$
3
AP EAPCET 2024 - 20th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$\int \sin ^{-1} \sqrt{\frac{x}{a+x}} d x=$
A
$(a+x) \tan ^{-1} \sqrt{\frac{x}{a}}-\sqrt{a x}+c$
B
$\frac{1}{a+x} \tan ^{-1}\left(\frac{x}{a}\right)-\sqrt{a x}+c$
C
$(a+x) \tan ^{-1}\left(\frac{a}{x}\right)+\sqrt{a x}+c$
D
$\sqrt{a+x} \tan ^{-1}\left(\frac{x}{a}\right)+a x+c$
4
AP EAPCET 2024 - 20th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$\int\limits_{\frac{-1}{24}}^{\frac{1}{24}} \sec x \log \left(\frac{1-x}{1+x}\right) d x=$
A
$\frac{\pi}{2}$
B
$\pi$
C
1
D
0
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