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

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

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integral of sqrt(3x^3)

\int 3 x^{3} d x

3 x^{2} x - \frac{3 3}{5} x^{\frac{5}{2}} + C

Solution steps

\int 3 x^{3} d x

Apply Integration By Parts

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

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

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

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

3 x x x^{2} = 3 x^{2} x

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

Add a constant to the solution

= 3 x^{2} x - \frac{3 3}{5} x^{\frac{5}{2}} + C

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