AP EAPCET 2024 - 21th May Morning Shift | Indefinite Integration Question 27 | Mathematics

If $n \geq 2$ is a natural number and $0<\theta<\frac{\pi}{2}$, then $\int \frac{\left(\cos ^n \theta-\cos \theta\right)^{1 / n}}{\cos ^{n+1} \theta} \sin \theta d \theta=$

$\frac{n}{n-1}\left(\cos ^{(1-n)} \theta-1\right)^2+c$

$\frac{n}{(n+1)(1-n)}\left(\cos ^{(1-n)} \theta-1\right)^{1+\frac{1}{n}}+c$

$\frac{1}{n-1}\left(\cos ^{(n-1)} \theta-1\right)^2+c$

$\frac{n}{1-n^2}\left(1-\cos ^{(1-n)} \theta\right)^{(n+1) / n}+c$

AP EAPCET 2024 - 20th May Evening Shift

MCQ (Single Correct Answer)

-0

If $\frac{x^2+3}{x^4+2 x^2+9}=\frac{A x+B}{x^2+a x+b}+\frac{C x+D}{x^2+c x+b}$, then $a A+b B+c C+D=$

-1

AP EAPCET 2024 - 20th May Evening Shift

MCQ (Single Correct Answer)

-0

$\int \frac{d x}{x\left(x^4+1\right)}=$

$\log \left(\frac{x}{x^4+1}\right)+c$

$\frac{3}{4} \log \left(x^4+1\right)+c$

$\frac{1}{3} \log \left(\frac{x^3}{x^4+1}\right)+c$

$\frac{1}{4} \log \left(\frac{x^4}{x^4+1}\right)+c$

AP EAPCET 2024 - 20th May Evening Shift

MCQ (Single Correct Answer)

-0

$\int \frac{d x}{\sqrt{\sin ^3 x \cos (x-a)}}=$

$\frac{1}{\cos \alpha} \sqrt{\cot x+\tan \alpha}+c$

$\frac{1}{\sqrt{\cos \alpha}} \sqrt{\cot x-\tan \alpha}+c$

$\frac{-1}{\sqrt{\sin \alpha}} \sqrt{\cot x+\tan \alpha}+c$

$\frac{-2}{\sqrt{\cos \alpha}} \sqrt{\cot x+\tan \alpha}+c$

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