What is the integral of x^{11}ln(5x^6) ?

The integral of x^{11}ln(5x^6) is 1/12 x^{12}(ln(5)+6ln(x))-(x^{12})/(24)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^{11}ln(5x^6)

\int x^{11} ln (5 x^{6}) d x

\frac{1}{12} x^{12} (ln (5) + 6 ln (x)) - \frac{x ^{12}}{24} + C

Solution steps

\int x^{11} ln (5 x^{6}) d x

Apply Integration By Parts

: \frac{1}{12} x^{12} ln (5 x^{6}) - \int \frac{x ^{11}}{2} d x

= \frac{1}{12} x^{12} ln (5 x^{6}) - \int \frac{x ^{11}}{2} d x

\int \frac{x ^{11}}{2} d x = \frac{x ^{12}}{24}

= \frac{1}{12} x^{12} ln (5 x^{6}) - \frac{x ^{12}}{24}

Simplify

ln (5 x^{6}) : 6 ln (x) + ln (5)

= \frac{1}{12} x^{12} (ln (5) + 6 ln (x)) - \frac{x ^{12}}{24}

Add a constant to the solution

= \frac{1}{12} x^{12} (ln (5) + 6 ln (x)) - \frac{x ^{12}}{24} + C

\int \frac{1 + y ^{2}}{2 - y} d y

\int (x^{2} y^{3}) d x

\int 5 x^{4} cos (x^{5}) d x

\int \frac{( x ^{2} + 4 )}{x} d x

\int (9 + tan^{2} (θ)) d θ

What is the integral of x^{11}ln(5x^6) ?
The integral of x^{11}ln(5x^6) is 1/12 x^{12}(ln(5)+6ln(x))-(x^{12})/(24)+C