What is the integral from 1 to 4 of (ln(x))/(x^3) ?

The integral from 1 to 4 of (ln(x))/(x^3) is 15/64-1/16 ln(2)

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integral from 1 to 4 of (ln(x))/(x^3)

\int_{1}^{4} \frac{ln ( x )}{x ^{3}} d x

\frac{15}{64} - \frac{1}{16} ln (2)

Decimal

0.19105 \dots

Solution steps

\int_{1}^{4} \frac{ln ( x )}{x ^{3}} d x

Apply Integration By Parts

: [- \frac{ln ( x )}{2 x ^{2}} - \int - \frac{1}{2 x ^{3}} d x]_{1}^{4}

= [- \frac{ln ( x )}{2 x ^{2}} - \int - \frac{1}{2 x ^{3}} d x]_{1}^{4}

\int - \frac{1}{2 x ^{3}} d x = \frac{1}{4 x ^{2}}

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

Compute the boundaries:

\frac{15}{64} - \frac{1}{16} ln (2)

= \frac{15}{64} - \frac{1}{16} ln (2)

\int_{0}^{l n (2)} 6 e^{2 t} d t

\int_{1}^{2} x + \frac{1}{x} d x

\int_{x^{2}}^{x} x y^{2} d y

\int_{2}^{3} 2^{- x} d x

\int_{0}^{1} x e^{t x} d x

What is the integral from 1 to 4 of (ln(x))/(x^3) ?
The integral from 1 to 4 of (ln(x))/(x^3) is 15/64-1/16 ln(2)