Mathematics

# Integrate the following function with respect to $x$$\dfrac{x.\sec^{2}{x^{2}}}{\sqrt{\tan^{3}{(x^{2})}}} ##### SOLUTION Let \displaystyle I= \int \dfrac{x.\sec^{2}{x^{2}}}{\sqrt{\tan^{3}{(x^{2})}}}.dx Put \tan (x^2)=t \therefore \sec^2 (x^2) \times 2x dx=dt \therefore x.sec^2(x^2)dx=\dfrac{dt}{2} \therefore I= \displaystyle \int \dfrac{1}{\sqrt{t^3}}.\dfrac{dt}{2} =\displaystyle \dfrac{1}{2} \int t^{-\dfrac{3}{2}}dt =\dfrac{1}{2}$$\dfrac{t^{-\dfrac{1}{2}}}{-\dfrac{1}{2}}+c$
$\dfrac{-1}{\sqrt t} +c$
$\dfrac{-1}{\sqrt{\tan(x^2)}} +c$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Single Correct Hard
Evalaute the integral
$\displaystyle \int_{0}^{\pi}xf(\sin x)dx$
• A. $2\pi$
• B. $\displaystyle \pi\int_{0}^{\pi}f(\cos x)dx$
• C. $\displaystyle \pi\int_{0}^{\pi}f(\sin x) dx$
• D. $\displaystyle \pi\int_{0}^{\pi/2}f(\cos x)dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Solve: $\displaystyle \int^{a}_{0} \dfrac{dx}{\sqrt{ax - x^2}}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium

$\int \dfrac{ \ sin2x}{1+ \ sinx} dx =$

• A. $log \ sin 2x +c$
• B.  $\frac{1}{2} log (1 + \ sin^2 x) + c$
• C. $\ tan^{-1} ( \ sin x)+c$
• D.  $2(1 + \sin x -log( 1+\ sin x) )+c$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
. Let $\displaystyle \mathrm{f}(\mathrm{x})=\frac{\mathrm{x}}{(1+\mathrm{x}^{\mathrm{n}})^{1/\mathrm{n}}}$ for $\mathrm{n}\geq 2$ and $\displaystyle \mathrm{g}(\mathrm{x})=\frac{(\mathrm{f}\mathrm{o}\mathrm{f}\mathrm{o}\ldots \mathrm{o}\mathrm{f})}{\mathrm{f}\mathrm{o}\mathrm{c}\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{s}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{s}}(\mathrm{x})$ . Then $\displaystyle \int \mathrm{x}^{\mathrm{n}-2}\mathrm{g}$ (x)dx equals

• A. $\displaystyle \frac{1}{\mathrm{n}-1}(1+\mathrm{n}\mathrm{x}^{\mathrm{n}})^{1\frac{1}{\mathrm{n}}}+\mathrm{K}$
• B. $\displaystyle \frac{1}{\mathrm{n}(\mathrm{n}+1)}(1+\mathrm{n}\mathrm{x}^{\mathrm{n}})^{1+\frac{1}{\mathrm{n}}}+\mathrm{K}$
• C. $\displaystyle \frac{1}{\mathrm{n}+1}(1+\mathrm{n}\mathrm{x}^{\mathrm{n}})^{1+\frac{1}{\mathrm{n}}}+\mathrm{K}$
• D. $\displaystyle \frac{1}{\mathrm{n}(\mathrm{n}-1)}(1+\mathrm{n}\mathrm{x}^{\mathrm{n}})^{1\frac{1}{\mathrm{n}}}+\mathrm{K}$

$\displaystyle\int { \left( \dfrac { x\cos { x } +\sin { x } }{ x\sin { x } } \right) dx }$