What is the integral from 1 to e of ln(x^7) ?

The integral from 1 to e of ln(x^7) is 7

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integral from 1 to e of ln(x^7)

\int_{1}^{e} ln (x^{7}) d x

7

Solution steps

\int_{1}^{e} ln (x^{7}) d x

Apply Integration By Parts

: [x ln (x^{7}) - \int 7 d x]_{1}^{e}

= [x ln (x^{7}) - \int 7 d x]_{1}^{e}

\int 7 d x = 7 x

= [x ln (x^{7}) - 7 x]_{1}^{e}

Apply log rule

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

assuming

x \geq 0

= [7 x ln (x) - 7 x]_{1}^{e}

Compute the boundaries:

7

= 7

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What is the integral from 1 to e of ln(x^7) ?
The integral from 1 to e of ln(x^7) is 7