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

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

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integral from 1 to 2 of ln(x^2)x

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

4 ln (2) - \frac{3}{2}

Decimal

1.27258 \dots

Solution steps

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

Apply Integration By Parts

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

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

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

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

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

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

Compute the boundaries:

4 ln (2) - \frac{3}{2}

= 4 ln (2) - \frac{3}{2}

\int_{2}^{3} \frac{x ^{2}}{x ^{3} - 2} d x

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\int_{3}^{6} ln (x) d x

\int_{4}^{7} 4 x d x

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