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Popular >

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

Solution

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

Solution

\frac{2}{7} ln^{\frac{7}{2}} (x) + C

Solution steps

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

Simplify

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

Apply u-substitution

: \int u^{\frac{5}{2}} d u

= \int u^{\frac{5}{2}} d u

Apply the Power Rule

: \frac{2}{7} u^{\frac{7}{2}}

= \frac{2}{7} u^{\frac{7}{2}}

Substitute back

u = ln (x)

= \frac{2}{7} ln^{\frac{7}{2}} (x)

Add a constant to the solution

= \frac{2}{7} ln^{\frac{7}{2}} (x) + C

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Frequently Asked Questions (FAQ)

What is the integral of ((ln(x))^{5/2})/x ?
The integral of ((ln(x))^{5/2})/x is 2/7 ln^{7/2}(x)+C