Final Answer
$-84x^{-\frac{1}{12}}+C_0$
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Step-by-step Solution
Problem to solve:
$\int\frac{7\sqrt[3]{x^{2}}}{\sqrt{x^3\sqrt{x}}}dx$
Specify the solving method
1
Simplify the expression inside the integral
$7\int\frac{1}{\sqrt[12]{x^{13}}}dx$
Learn how to solve integrals of rational functions problems step by step online.
$7\int\frac{1}{\sqrt[12]{x^{13}}}dx$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((7x^2/3)/((x^3x^1/2)^1/2))dx. Simplify the expression inside the integral. Rewrite the exponent using the power rule \frac{a^m}{a^n}=a^{m-n}, where in this case m=0. Apply the power rule for integration, \displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}, where n represents a number or constant function, such as -\frac{13}{12}. Simplify the expression inside the integral.
Final Answer
$-84x^{-\frac{1}{12}}+C_0$