What is the integral from 1 to 2 of xlog_{5}(x) ?

The integral from 1 to 2 of xlog_{5}(x) is 2log_{5}(2)-3/(4ln(5))

Popular >

integral from 1 to 2 of xlog_{5}(x)

\int_{1}^{2} x lo g_{5} (x) d x

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

Decimal

0.39535 \dots

Solution steps

\int_{1}^{2} x lo g_{5} (x) d x

Apply Integration By Parts

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

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

\int \frac{x}{2 ln ( 5 )} d x = \frac{x ^{2}}{4 ln ( 5 )}

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

Compute the boundaries:

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

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

\int_{- 1}^{0} \frac{1}{e ^{x} + 1} d x

\int_{- 1}^{1} (x^{5} - x^{7}) d x

\int_{0}^{3} 4 t d t

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

\int_{0}^{5} 4 e^{x} d x

What is the integral from 1 to 2 of xlog_{5}(x) ?
The integral from 1 to 2 of xlog_{5}(x) is 2log_{5}(2)-3/(4ln(5))