What is the integral of sqrt(x)In^2x ?

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

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integral of sqrt(x)In^2x

\int x I n^{2} x d x

I n^{2} \frac{2}{5} x^{\frac{5}{2}} + C

Solution steps

\int x I n^{2} x d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= I n^{2} \cdot \int x x d x

Simplify

x x : x^{\frac{3}{2}}

= I n^{2} \cdot \int x^{\frac{3}{2}} d x

Apply the Power Rule

= I n^{2} \frac{2}{5} x^{\frac{5}{2}}

Add a constant to the solution

= I n^{2} \frac{2}{5} x^{\frac{5}{2}} + C

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