TS EAMCET 2022 (Online) 19th July Morning Shift | Indefinite Integration Question 93 | Mathematics

Given that $\frac{d}{d x}\left(\tan ^{-1} x\right)=\frac{1}{1+x^2}$ and $\frac{d}{d x}\left(\sin h^{-1} x\right)=\frac{1}{\sqrt{1+x^2}}$. Then, $\int \frac{3 x^6-2 x^4+x^2-2}{x^2+1} d x=$

$\frac{3}{7} x^7-\frac{2}{5} x^5+\frac{1}{3} x^3-2 x+c$

$\frac{\frac{3}{7} x^7-\frac{2}{5} x^5+\frac{1}{3} x^3-2 x}{\frac{x^3}{3}+x}+c$

$\frac{3}{5} x^5-\frac{5}{3} x^3+6 x-8 \tan ^{-1} x+c$

$\frac{3}{5} x^5-\frac{5}{3} x^3+6 x-8 \sin h^{-1} x+c$

TS EAMCET 2022 (Online) 19th July Morning Shift

MCQ (Single Correct Answer)

-0

$$ \int \frac{\sin x \cdot \sec ^2 x-\tan x \cdot \sin x+\cos x}{(1-\cos 2 x)} d x= $$

$\frac{1}{2}\left[\sec x-\operatorname{cosec} x-\log \left|\tan \left(\frac{x}{2}\right) \tan \left(\frac{\pi}{4}+\frac{x}{2}\right)\right|\right]+C$

$\sec x-\operatorname{cosec} x+\log \left|\frac{\tan \left(\frac{\pi}{2}\right)}{\tan \left(\frac{\pi}{4}+\frac{x}{2}\right)}\right|+C$

$\frac{1}{2}\left[\sec x-\operatorname{cosec} x-\log \left|\frac{\tan \left(\frac{\pi}{4}+\frac{x}{2}\right)}{\tan \left(\frac{x}{2}\right)}\right|\right]+C$

$\sec x+\operatorname{cosec} x-\log \left|\tan \left(\frac{x}{2}\right)\right|+C$

TS EAMCET 2022 (Online) 19th July Morning Shift

MCQ (Single Correct Answer)

-0

If $f(x)=\int \frac{16 x^7+5 x^{10}}{\left(x^3+2+3 x^8\right)^2} d x(x \geq 0)$ and $f(0)=1$, then the value of $f(-1)$ is

$\frac{7}{6}$

$\frac{5}{4}$

$\frac{-3}{4}$

$\frac{-5}{6}$

TS EAMCET 2022 (Online) 18th July Evening Shift

MCQ (Single Correct Answer)

-0

$$ \begin{aligned} & \text { If } \int \frac{(x+3)}{(x-1)^2(2 x-1)} d x \\ & =\frac{A}{x-1}+B \log (2 x-1)+C \log (x-1)+k, \text { then } A+B+C= \end{aligned} $$

-4

-11

PREVIOUS NEXT

TS EAMCET Subjects

Browse all chapters by subject