What is the integral of 3xln(x^8) ?

The integral of 3xln(x^8) is 3(4x^2ln(x)-2x^2)+C

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integral of 3xln(x^8)

\int 3 x ln (x^{8}) d x

3 (4 x^{2} ln (x) - 2 x^{2}) + C

Solution steps

\int 3 x ln (x^{8}) d x

Take the constant out:

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

= 3 \cdot \int x ln (x^{8}) d x

Apply Integration By Parts

= 3 (\frac{1}{2} x^{2} ln (x^{8}) - \int 4 x d x)

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

= 3 (\frac{1}{2} x^{2} ln (x^{8}) - 2 x^{2})

\frac{1}{2} x^{2} ln (x^{8}) = 4 x^{2} ln (x)

= 3 (4 x^{2} ln (x) - 2 x^{2})

Add a constant to the solution

= 3 (4 x^{2} ln (x) - 2 x^{2}) + C

What is the integral of 3xln(x^8) ?
The integral of 3xln(x^8) is 3(4x^2ln(x)-2x^2)+C