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

The integral of ((ln(x))^{7/2})/x is 2/9 ln^{9/2}(x)+C

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integral of ((ln(x))^{7/2})/x

\int \frac{( ln ( x ) ) ^{\frac{7}{2}}}{x} d x

\frac{2}{9} ln^{\frac{9}{2}} (x) + C

Solution steps

\int \frac{( ln ( x ) ) ^{\frac{7}{2}}}{x} d x

Simplify

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

Apply u-substitution

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

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

Apply the Power Rule

: \frac{2}{9} u^{\frac{9}{2}}

= \frac{2}{9} u^{\frac{9}{2}}

Substitute back

u = ln (x)

= \frac{2}{9} ln^{\frac{9}{2}} (x)

Add a constant to the solution

= \frac{2}{9} ln^{\frac{9}{2}} (x) + C

\int_{- \infty}^{2} e^{x} d x

x \to 2 lim (x^{3} + x^{2} + x)

x \to 0 lim (\frac{sin ( 7 x )}{tan ( 11 x )})

\int x^{2} e^{19 x} d x

\frac{d}{d x} (\frac{x - 3}{x ^{2} - 5})

What is the integral of ((ln(x))^{7/2})/x ?
The integral of ((ln(x))^{7/2})/x is 2/9 ln^{9/2}(x)+C