Mathematics

# f(x) = $\displaystyle \int \frac{dx}{x^{2}\left ( 1+x^{5} \right )^{4/5}}$, taking c = 0, value of $|f(1)|=$

2

##### SOLUTION
$\displaystyle I=\int \frac{dx}{x^{2}\left ( 1+x^{5} \right )^{4/5}} \int \frac{dx}{x^{6}\left ( \frac{1}{x^{5}+1} \right )^{4/5}}$
$\displaystyle Let\:t=1+\frac{1}{x^{5}}or\:dt=\frac{5dx}{x^{6}}$
$\displaystyle \therefore I=-\frac{1}{5}\int \frac{dt}{t^{4/5}}=-t^{3/5}+c=-\left ( 1+\frac{1}{x^{5}} \right )^{3/5}+c$
$\displaystyle=-\left(\frac{1+x^{5}}{x}\right)^{\tfrac{3}{5}}+c$

$f(x)=-\left(\dfrac{1+x^{5}}{x}\right)^{\tfrac{3}{5}}\Rightarrow f(1)=-2\Rightarrow |f(1)|=2$

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One Word Hard Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 111

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