Mathematics

# $\int \dfrac{{{x^5}}}{{\sqrt {1 - {x^{12}}} }}\;dx$

##### SOLUTION
$\frac{x^{5}}{\sqrt{1-x^{12}}}dx\Rightarrow \int \frac{x^{5}}{1-(x^{6})^{2}}dx$        $x^{6}=t$
$=\frac{1}{6}\int \frac{1}{\sqrt{1-t^{2}}}dt$         $6x^{5}=\frac{dt}{dx}$
$=\frac{1}{6}sin^{-1}(t)=\frac{1}{6} sin^{-1}(x^{6})+c$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 One Word Medium
Evaluate:$\displaystyle \int \frac{(1-3x)}{(3x^{2}+4x+2)}dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
$\displaystyle \int_{-\pi/2}^{\pi/2} (sin^3x+cos^3x)dx$ equals-
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• C. $2/3$
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Q3 Single Correct Medium
$\displaystyle \int_{0}^{1}\frac{2^{x+1}-3^{x-1}}{6^{x}}dx$
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Q4 Subjective Hard
Evaluate:
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