What is the integral of sqrt(4x^3) ?

The integral of sqrt(4x^3) is 2x^2sqrt(x)-6/5 x^{5/2}+C

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integral of sqrt(4x^3)

\int 4 x^{3} d x

2 x^{2} x - \frac{6}{5} x^{\frac{5}{2}} + C

Solution steps

\int 4 x^{3} d x

Apply Integration By Parts

: 2 x x x^{2} - \int \frac{3 x ^{\frac{5}{2}}}{x ^{2}} d x

= 2 x x x^{2} - \int \frac{3 x ^{\frac{5}{2}}}{x ^{2}} d x

\int \frac{3 x ^{\frac{5}{2}}}{x ^{2}} d x = \frac{6}{5} x^{\frac{5}{2}}

= 2 x x x^{2} - \frac{6}{5} x^{\frac{5}{2}}

2 x x x^{2} = 2 x^{2} x

= 2 x^{2} x - \frac{6}{5} x^{\frac{5}{2}}

Add a constant to the solution

= 2 x^{2} x - \frac{6}{5} x^{\frac{5}{2}} + C

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What is the integral of sqrt(4x^3) ?
The integral of sqrt(4x^3) is 2x^2sqrt(x)-6/5 x^{5/2}+C