What is the integral from 5 to 8 of 10log_{4}(x) ?

The integral from 5 to 8 of 10log_{4}(x) is 10(-5log_{4}(5)-3/(2ln(2))+12)

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integral from 5 to 8 of 10log_{4}(x)

\int_{5}^{8} 10 lo g_{4} (x) d x

10 (- 5 lo g_{4} (5) - \frac{3}{2 ln ( 2 )} + 12)

Decimal

40.31137 \dots

Solution steps

\int_{5}^{8} 10 lo g_{4} (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 10 \cdot \int_{5}^{8} lo g_{4} (x) d x

Apply Integration By Parts

: [x lo g_{4} (x) - \int \frac{1}{2 ln ( 2 )} d x]_{5}^{8}

= 10 [x lo g_{4} (x) - \int \frac{1}{2 ln ( 2 )} d x]_{5}^{8}

\int \frac{1}{2 ln ( 2 )} d x = \frac{1}{2 ln ( 2 )} x

= 10 [x lo g_{4} (x) - \frac{1}{2 ln ( 2 )} x]_{5}^{8}

Compute the boundaries:

- 5 lo g_{4} (5) - \frac{3}{2 ln ( 2 )} + 12

= 10 (- 5 lo g_{4} (5) - \frac{3}{2 ln ( 2 )} + 12)

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What is the integral from 5 to 8 of 10log_{4}(x) ?
The integral from 5 to 8 of 10log_{4}(x) is 10(-5log_{4}(5)-3/(2ln(2))+12)