What is the integral from 7 to 15 of ln(x^2) ?

The integral from 7 to 15 of ln(x^2) is 30ln(15)-16-14ln(7)

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integral from 7 to 15 of ln(x^2)

\int_{7}^{15} ln (x^{2}) d x

30 ln (15) - 16 - 14 ln (7)

Decimal

37.99876 \dots

Solution steps

\int_{7}^{15} ln (x^{2}) d x

Apply Integration By Parts

: [x ln (x^{2}) - \int 2 d x]_{7}^{15}

= [x ln (x^{2}) - \int 2 d x]_{7}^{15}

\int 2 d x = 2 x

= [x ln (x^{2}) - 2 x]_{7}^{15}

Apply log rule

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

assuming

x \geq 0

= [2 x ln (x) - 2 x]_{7}^{15}

Compute the boundaries:

30 ln (15) - 16 - 14 ln (7)

= 30 ln (15) - 16 - 14 ln (7)

y^{^{'}} = \frac{x ^{8} - 2 y}{x}

ln (csc (x) - cot (x))

\int \frac{x + 5}{x ^{2} - 16} d x

x \to 0 lim (x^{x^{6}})

f (x) = \frac{x ^{6}}{8 ^{x}}

What is the integral from 7 to 15 of ln(x^2) ?
The integral from 7 to 15 of ln(x^2) is 30ln(15)-16-14ln(7)