What is the integral from 1 to 5 of (ln(x))/(x^7) ?

The integral from 1 to 5 of (ln(x))/(x^7) is 434/15625-1/93750 ln(5)

Popular >

integral from 1 to 5 of (ln(x))/(x^7)

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

\frac{434}{15625} - \frac{1}{93750} ln (5)

Decimal

0.02775 \dots

Solution steps

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

Apply Integration By Parts

: [- \frac{ln ( x )}{6 x ^{6}} - \int - \frac{1}{6 x ^{7}} d x]_{1}^{5}

= [- \frac{ln ( x )}{6 x ^{6}} - \int - \frac{1}{6 x ^{7}} d x]_{1}^{5}

\int - \frac{1}{6 x ^{7}} d x = \frac{1}{36 x ^{6}}

= [- \frac{ln ( x )}{6 x ^{6}} - \frac{1}{36 x ^{6}}]_{1}^{5}

Compute the boundaries:

\frac{434}{15625} - \frac{1}{93750} ln (5)

= \frac{434}{15625} - \frac{1}{93750} ln (5)

\frac{d}{d x} (\frac{3}{2} x^{\frac{5}{3}} - \frac{5 x}{4} + 7 x^{2} - \frac{6}{x ^{5}} + 6)

y = (3 x - 2 x^{2})^{3} \frac{d y}{d x}

\frac{d y}{d x} = x^{7} e^{x^{8}}

x \to 0 lim (x e^{\frac{1}{x}})

\int \frac{3}{x ^{2} + 10 x + 29} d x

What is the integral from 1 to 5 of (ln(x))/(x^7) ?
The integral from 1 to 5 of (ln(x))/(x^7) is 434/15625-1/93750 ln(5)