TS EAMCET 2020 (Online) 10th September Morning Shift | Indefinite Integration Question 126 | Mathematics

If $\frac{4 x^2+5 x^4+7}{\left(x^2+1\right)\left(x^4+x^2+1\right)}=\frac{A x+B}{x^2+1} +\frac{C x^3+D x^2+E x+F}{x^4+x^2+1}$, then $B+2(D+F+E)-C \cdot A=$

-3

TS EAMCET 2020 (Online) 10th September Morning Shift

MCQ (Single Correct Answer)

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$$ \int \frac{y^2+\sqrt[3]{y^4}+\sqrt[6]{y^2}}{y\left(1+\sqrt[3]{y^2}\right)} d y= $$

$\frac{3}{4} \sqrt[3]{y^4}+3 \tan ^{-1}(\sqrt[3]{y})+C$

$\frac{3}{2} y^{2 / 3}+6 \tan ^{-1}\left(\sqrt[6]{y^2}\right)+C$

$\frac{2}{3 \sqrt[3]{y^2}}+6 \log \left(1+y^2\right)+C$

$\frac{3}{1+y}+\tan ^{-1}\left(\sqrt[3]{y^2}\right)+C$

TS EAMCET 2020 (Online) 10th September Morning Shift

MCQ (Single Correct Answer)

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For $k \in(1, \infty), \int \frac{1}{1+k \cos x} d x=$

$\frac{2}{\sqrt{1+k^2}} \tan ^{-1}\left(\sqrt{\frac{1-k}{1+k}} \tan \frac{x}{2}\right)+C$

$\frac{1}{\sqrt{k^2-1}} \log \left(\frac{\sqrt{k+1}+\sqrt{k-1} \tan \frac{x}{2}}{\sqrt{k+1}-\sqrt{k-1}}\right)+C$

$\frac{1}{\sqrt{k^2+1}} \log ^{-1}\left(\frac{\sqrt{k+1}+\sqrt{k-1} \tan \frac{x}{2}}{\sqrt{k+1}-\sqrt{k-1} \tan \frac{x}{2}}\right)+C$

$\frac{1}{\sqrt{k^2-1}} \tan ^{-1}\left(\frac{\sqrt{k-1} \cos \frac{x}{2}+\sqrt{k-1} \sin \frac{x}{2}}{\sqrt{k+1} \cos \frac{x}{2}-\sqrt{k-1} \sin \frac{x}{2}}\right)+C$

TS EAMCET 2020 (Online) 10th September Morning Shift

MCQ (Single Correct Answer)

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$$ \int e^{-3 x}\left(x^2+\sin 4 x\right) d x= $$

$-e^{-3 x}\left(\frac{x^2}{3}+\frac{2 x}{9}+\frac{2}{27}+\frac{3}{25} \sin 4 x+\frac{4}{25} \cos 4 x\right)+C$

$-e^{-3 x}\left(\frac{x^2}{3}-\frac{2 x}{9}+\frac{2}{27}+\frac{3}{25} \sin 4 x+\frac{4}{25} \cos 4 x\right)+C$

$-e^{-3 x}\left(\frac{x^2}{3}+\frac{2 x}{9}+\frac{2}{27}+\frac{3}{25} \sin 4 x-\frac{4}{25} \cos 4 x\right)+C$

$-e^{-3 x}\left(\frac{x^2}{3}-\frac{2 x}{9}+\frac{2}{27}+\frac{3}{25} \sin 4 x-\frac{4}{25} \cos 4 x\right)+C$

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