What is the integral of xn(x^2) ?

The integral of xn(x^2) is d(x^2ln(x)-(x^2)/2)+C

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integral of xn(x^2)

\int x d ln (x^{2}) d x

d (x^{2} ln (x) - \frac{x ^{2}}{2}) + C

Solution steps

\int x d ln (x^{2}) d x

Take the constant out:

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

= d \cdot \int x ln (x^{2}) d x

Apply Integration By Parts

: \frac{1}{2} x^{2} ln (x^{2}) - \int x d x

= d (\frac{1}{2} x^{2} ln (x^{2}) - \int x d x)

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

= d (\frac{1}{2} x^{2} ln (x^{2}) - \frac{x ^{2}}{2})

\frac{1}{2} x^{2} ln (x^{2}) = x^{2} ln (x)

= d (x^{2} ln (x) - \frac{x ^{2}}{2})

Add a constant to the solution

= d (x^{2} ln (x) - \frac{x ^{2}}{2}) + C

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What is the integral of xn(x^2) ?
The integral of xn(x^2) is d(x^2ln(x)-(x^2)/2)+C