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