What is the integral from 3 to 12 of ln(x^8) ?

The integral from 3 to 12 of ln(x^8) is 24ln(6912)-72

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integral from 3 to 12 of ln(x^8)

\int_{3}^{12} ln (x^{8}) d x

24 ln (6912) - 72

Decimal

140.18434 \dots

Solution steps

\int_{3}^{12} ln (x^{8}) d x

Apply Integration By Parts

: [x ln (x^{8}) - \int 8 d x]_{3}^{12}

= [x ln (x^{8}) - \int 8 d x]_{3}^{12}

\int 8 d x = 8 x

= [x ln (x^{8}) - 8 x]_{3}^{12}

Apply log rule

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

assuming

x \geq 0

= [8 x ln (x) - 8 x]_{3}^{12}

Compute the boundaries:

96 ln (12) - 72 - 24 ln (3)

= 96 ln (12) - 72 - 24 ln (3)

Simplify

= 24 ln (6912) - 72

\int \frac{sin ( n x )}{n} d x

y^{^{'}} = - \frac{1}{2} y

\int (\frac{12}{x} + \frac{x}{12}) d x

x y^{^{'}} + 3 y = \frac{2 e ^{4 x}}{x ^{2}}

\frac{d}{d x} (a x^{2} e^{- x})

What is the integral from 3 to 12 of ln(x^8) ?
The integral from 3 to 12 of ln(x^8) is 24ln(6912)-72