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

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

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integral of 2xln(x^2)

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

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

Solution steps

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

Take the constant out:

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

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

Apply Integration By Parts

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

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

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

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

Simplify

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

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

Add a constant to the solution

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

\int \frac{cos ^{3} ( x )}{sin ^{2} ( x )} d x

\int (\frac{7}{x} + \frac{15}{x ^{6}}) d x

y = sin (2 x) cos (2 x)

\frac{\partial}{\partial x} ((\frac{x + 2}{y + 1})^{\frac{1}{2}})

e^{a s}

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