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Popular >

integral of (ln(2x))/(x^5)

Solution

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

Solution

- \frac{ln ( 2 x )}{4 x ^{4}} - \frac{1}{16 x ^{4}} + C

Solution steps

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

Apply Integration By Parts

: - \frac{ln ( 2 x )}{4 x ^{4}} - \int - \frac{1}{4 x ^{5}} d x

= - \frac{ln ( 2 x )}{4 x ^{4}} - \int - \frac{1}{4 x ^{5}} d x

\int - \frac{1}{4 x ^{5}} d x = \frac{1}{16 x ^{4}}

= - \frac{ln ( 2 x )}{4 x ^{4}} - \frac{1}{16 x ^{4}}

Add a constant to the solution

= - \frac{ln ( 2 x )}{4 x ^{4}} - \frac{1}{16 x ^{4}} + C

Popular Examples

integral of (8x^3-12x^2+7x+2)/(2x-2)

\int \frac{8 x ^{3} - 12 x ^{2} + 7 x + 2}{2 x - 2} d x

integral of 6/x+5/(x^2)

\int \frac{6}{x} + \frac{5}{x ^{2}} d x

integral of (u+2)/(5u+6)

\int \frac{u + 2}{5 u + 6} d u

integral of 1-6sin(3x)

\int 1 - 6 sin (3 x) d x

integral of 1/((2y+3))

\int \frac{1}{( 2 y + 3 )} d y

Frequently Asked Questions (FAQ)

What is the integral of (ln(2x))/(x^5) ?
The integral of (ln(2x))/(x^5) is -(ln(2x))/(4x^4)-1/(16x^4)+C