What is the integral from 1 to 3 of 2xln(x^2) ?

The integral from 1 to 3 of 2xln(x^2) is 2(9ln(3)-4)

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integral from 1 to 3 of 2xln(x^2)

\int_{1}^{3} 2 x ln (x^{2}) d x

2 (9 ln (3) - 4)

Solution steps

\int_{1}^{3} 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_{1}^{3} x ln (x^{2}) d x

Apply Integration By Parts

: [\frac{1}{2} x^{2} ln (x^{2}) - \int x d x]_{1}^{3}

= 2 [\frac{1}{2} x^{2} ln (x^{2}) - \int x d x]_{1}^{3}

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

= 2 [\frac{1}{2} x^{2} ln (x^{2}) - \frac{x ^{2}}{2}]_{1}^{3}

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

= 2 [x^{2} ln (x) - \frac{x ^{2}}{2}]_{1}^{3}

Compute the boundaries:

9 ln (3) - 4

= 2 (9 ln (3) - 4)

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What is the integral from 1 to 3 of 2xln(x^2) ?
The integral from 1 to 3 of 2xln(x^2) is 2(9ln(3)-4)