What is the integral from 1 to e of ln(x^4) ?

The integral from 1 to e of ln(x^4) is 4

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integral from 1 to e of ln(x^4)

\int_{1}^{e} ln (x^{4}) d x

4

Solution steps

\int_{1}^{e} ln (x^{4}) d x

Apply Integration By Parts

: [x ln (x^{4}) - \int 4 d x]_{1}^{e}

= [x ln (x^{4}) - \int 4 d x]_{1}^{e}

\int 4 d x = 4 x

= [x ln (x^{4}) - 4 x]_{1}^{e}

Apply log rule

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

assuming

x \geq 0

= [4 x ln (x) - 4 x]_{1}^{e}

Compute the boundaries:

4

= 4

\int_{0}^{3} x^{2} - 6 x + 8 d x

\int_{0}^{\infty} x^{p} d x

\int_{0}^{3} t^{2} d t

\int_{0}^{4} 8 y d y

\int_{i}^{1} (z + 1)^{2} d z

What is the integral from 1 to e of ln(x^4) ?
The integral from 1 to e of ln(x^4) is 4