What is the integral from 7 to 12 of ln(x^3) ?

The integral from 7 to 12 of ln(x^3) is 36ln(12)-15-21ln(7)

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integral from 7 to 12 of ln(x^3)

\int_{7}^{12} ln (x^{3}) d x

36 ln (12) - 15 - 21 ln (7)

Decimal Notation

33.59252 \dots

Solution steps

\int_{7}^{12} ln (x^{3}) d x

Apply Integration By Parts

: [x ln (x^{3}) - \int 3 d x]_{7}^{12}

= [x ln (x^{3}) - \int 3 d x]_{7}^{12}

\int 3 d x = 3 x

= [x ln (x^{3}) - 3 x]_{7}^{12}

Apply log rule

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

assuming

x \geq 0

= [3 x ln (x) - 3 x]_{7}^{12}

Compute the boundaries:

36 ln (12) - 15 - 21 ln (7)

= 36 ln (12) - 15 - 21 ln (7)

\frac{- 8 x - 2}{9 x - 4}

\frac{d}{d x} (x e^{- t})

\frac{\partial}{\partial x} (4 x^{3} + y)

5 tan (5 x)

\int \frac{2}{sec ( x ) sin ^{3} ( x )} d x

What is the integral from 7 to 12 of ln(x^3) ?
The integral from 7 to 12 of ln(x^3) is 36ln(12)-15-21ln(7)