What is the integral from 1 to 12 of ln(x^6) ?

The integral from 1 to 12 of ln(x^6) is 72ln(12)-66

Popular >

integral from 1 to 12 of ln(x^6)

\int_{1}^{12} ln (x^{6}) d x

72 ln (12) - 66

Decimal

112.91327 \dots

Solution steps

\int_{1}^{12} ln (x^{6}) d x

Apply Integration By Parts

: [x ln (x^{6}) - \int 6 d x]_{1}^{12}

= [x ln (x^{6}) - \int 6 d x]_{1}^{12}

\int 6 d x = 6 x

= [x ln (x^{6}) - 6 x]_{1}^{12}

Apply log rule

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

assuming

x \geq 0

= [6 x ln (x) - 6 x]_{1}^{12}

Compute the boundaries:

72 ln (12) - 66

= 72 ln (12) - 66

\int_{0}^{0.8} \frac{1}{1 - x ^{2}} d x

\int_{0}^{\frac{π}{2}} 4 sin (x) cos (x) d x

\int_{- 1}^{1} \frac{- x + 1}{x ^{2} - 4} d x

\int_{1}^{0} (3 x^{2} + x - 5) d x

\int_{0}^{1} x (3 x^{2} - 4)^{3} d x

What is the integral from 1 to 12 of ln(x^6) ?
The integral from 1 to 12 of ln(x^6) is 72ln(12)-66