What is the integral of (xsqrt(x))/(\sqrt[4]{x^3)} ?

The integral of (xsqrt(x))/(\sqrt[4]{x^3)} is 4/7 x^{7/4}+C

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integral of (xsqrt(x))/(\sqrt[4]{x^3)}

\int \frac{x x}{4 x ^{3}} d x

\frac{4}{7} x^{\frac{7}{4}} + C

Solution steps

\int \frac{x x}{4 x ^{3}} d x

x x = x^{2} (x)

= \int \frac{x ^{2} x}{4 x ^{3}} d x

Simplify

x^{2} (x) : x^{3}

= \int \frac{x ^{3}}{4 x ^{3}} d x

Simplify

\frac{x ^{3}}{4 x ^{3}} : 4 x^{3}

= \int 4 x^{3} d x

4 x^{3} = x^{\frac{3}{4}},

assuming

x \geq 0

= \int x^{\frac{3}{4}} d x

Apply the Power Rule

: \frac{4}{7} x^{\frac{7}{4}}

= \frac{4}{7} x^{\frac{7}{4}}

Add a constant to the solution

= \frac{4}{7} x^{\frac{7}{4}} + C

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What is the integral of (xsqrt(x))/(\sqrt[4]{x^3)} ?
The integral of (xsqrt(x))/(\sqrt[4]{x^3)} is 4/7 x^{7/4}+C