What is the integral of x^9ln(9x^5) ?

The integral of x^9ln(9x^5) is 1/10 x^{10}(2ln(3)+5ln(x))-(x^{10})/(20)+C

Popular >

integral of x^9ln(9x^5)

\int x^{9} ln (9 x^{5}) d x

\frac{1}{10} x^{10} (2 ln (3) + 5 ln (x)) - \frac{x ^{10}}{20} + C

Solution steps

\int x^{9} ln (9 x^{5}) d x

Apply Integration By Parts

: \frac{1}{10} x^{10} ln (9 x^{5}) - \int \frac{x ^{9}}{2} d x

= \frac{1}{10} x^{10} ln (9 x^{5}) - \int \frac{x ^{9}}{2} d x

\int \frac{x ^{9}}{2} d x = \frac{x ^{10}}{20}

= \frac{1}{10} x^{10} ln (9 x^{5}) - \frac{x ^{10}}{20}

\frac{1}{10} x^{10} ln (9 x^{5}) = \frac{1}{10} x^{10} (2 ln (3) + 5 ln (x))

= \frac{1}{10} x^{10} (2 ln (3) + 5 ln (x)) - \frac{x ^{10}}{20}

Add a constant to the solution

= \frac{1}{10} x^{10} (2 ln (3) + 5 ln (x)) - \frac{x ^{10}}{20} + C

\int \frac{e ^{3 t}}{4 - e ^{6 t}} d t

\int \frac{4 x}{9 - x ^{4}} d x

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

\int sec^{2} (x) - tan^{2} (x) d x

\int \frac{x}{50} d x

What is the integral of x^9ln(9x^5) ?
The integral of x^9ln(9x^5) is 1/10 x^{10}(2ln(3)+5ln(x))-(x^{10})/(20)+C