Step-by-step Solution

Integral of 1/(x^7^(1/5))

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$-\frac{5}{2}x^{-\frac{2}{5}}+C_0$

Step-by-step explanation

Problem to solve:

$\int\frac{1}{\sqrt[5]{x^7}}dx$
1

Applying the power of a power property

$\int\frac{1}{\sqrt[5]{x^{7}}}dx$
2

Rewrite the exponent using the power rule $\frac{a^m}{a^n}=a^{m-n}$, where in this case $m=0$

$\int x^{-\frac{7}{5}}dx$

$-\frac{5}{2}x^{-\frac{2}{5}}+C_0$

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$\int\frac{1}{\sqrt[5]{x^7}}dx$

Main topic:

Integral calculus

~ 0.78 seconds