TS EAMCET 2020 (Online) 11th September Evening Shift | Indefinite Integration Question 113 | Mathematics

If the partial fractions decomposition of $\frac{x^4+24 x^2+28}{\left(x^2+1\right)^3}$ is $\frac{A}{x^2+1}+\frac{B}{\left(x^2+1\right)^2}+\frac{C}{\left(x^2+1\right)^3}$ then $B-2 A+C=$

TS EAMCET 2020 (Online) 11th September Evening Shift

MCQ (Single Correct Answer)

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$$ \int \frac{x^2}{\left(\sqrt{4-x^2}\right)^3} d x= $$

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

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

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

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

TS EAMCET 2020 (Online) 11th September Evening Shift

MCQ (Single Correct Answer)

-0

$$ \int \frac{d x}{x \ln (x) \ln ^2(x) \ln ^3(x) \ldots \ln ^m(x)}=\frac{(\ln (x))^K}{K}+C \Rightarrow 2 K= $$

$(m+1)(m+2)$

$(2-m)(1-m)$

$(m+1)(2-m)$

$(m+2)(1-m)$

TS EAMCET 2020 (Online) 11th September Evening Shift

MCQ (Single Correct Answer)

-0

If $I_m=\int x^m \cos n x d x=g(x)-\frac{m(m-1)}{n^2} I_{m-2}$, then $g(x)=$

$\frac{x^m \sin n x}{n}+\frac{m(m-1) x^{m-1} \cos n x}{n^2}$

$\frac{x^m \cos n x}{n}+\frac{x^{m-1} m(m-1)}{n^2} \sin n x$

$\frac{m}{n} \sin n x+\frac{m}{n^2} x^{m-1} \cos n x$

$\frac{x^m \sin n x}{n}+\frac{m}{n^2} x^{m-1} \cos n x$

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