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Step-by-step Solution

Integrate 7x^(4/3)+1/3x^(-2/3)+6/5x^(1/5) from 0 to 1

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Answer

$\int_{0}^{1}7\sqrt[3]{x^{4}}dx+\int_{0}^{1}\frac{1}{3}x^{-\frac{2}{3}}dx+\int_{0}^{1}\frac{6}{5}\sqrt[5]{x}dx$

Step-by-step explanation

Problem to solve:

$\int_{0}^{1}\left(7x^{\frac{4}{3}}+\frac{1}{3} x^{-\frac{2}{3}}+\frac{6}{5} x^{\frac{1}{5}}\right)dx$
1

Multiply $-1$ times $\frac{2}{3}$

$\int_{0}^{1}\left(7\sqrt[3]{x^{4}}+\frac{1}{3}x^{-\frac{2}{3}}+\frac{6}{5}\sqrt[5]{x}\right)dx$
2

The integral of a sum of two or more functions is equal to the sum of their integrals

$\int_{0}^{1}7\sqrt[3]{x^{4}}dx+\int_{0}^{1}\frac{1}{3}x^{-\frac{2}{3}}dx+\int_{0}^{1}\frac{6}{5}\sqrt[5]{x}dx$

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Answer

$\int_{0}^{1}7\sqrt[3]{x^{4}}dx+\int_{0}^{1}\frac{1}{3}x^{-\frac{2}{3}}dx+\int_{0}^{1}\frac{6}{5}\sqrt[5]{x}dx$

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$\int_{0}^{1}\left(7x^{\frac{4}{3}}+\frac{1}{3} x^{-\frac{2}{3}}+\frac{6}{5} x^{\frac{1}{5}}\right)dx$

Main topic:

Integral calculus

Time to solve it:

~ 0.4 seconds

Related topics:


Integral calculus