What is the integral from 4 to 8 of ln(x^2) ?

The integral from 4 to 8 of ln(x^2) is 32ln(2)-8

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integral from 4 to 8 of ln(x^2)

\int_{4}^{8} ln (x^{2}) d x

32 ln (2) - 8

Solution steps

\int_{4}^{8} ln (x^{2}) d x

Apply Integration By Parts

: [x ln (x^{2}) - \int 2 d x]_{4}^{8}

= [x ln (x^{2}) - \int 2 d x]_{4}^{8}

\int 2 d x = 2 x

= [x ln (x^{2}) - 2 x]_{4}^{8}

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

= [2 x ln (x) - 2 x]_{4}^{8}

Compute the boundaries:

32 ln (2) - 8

= 32 ln (2) - 8

\int_{0}^{\frac{π}{3}} x sec^{2} (x) d x

2 x, x^{2}

\int \frac{2 x + y + z}{( x + y ) ( x + z )} d x

8 x^{2} - 7 x, at 9

y^{3} - (6 x + 8) + 3 x y^{2} y^{^{'}} = 0

What is the integral from 4 to 8 of ln(x^2) ?
The integral from 4 to 8 of ln(x^2) is 32ln(2)-8