What is the integral of x^{15}ln(8x^8) ?

The integral of x^{15}ln(8x^8) is 1/16 x^{16}(3ln(2)+8ln(x))-(x^{16})/(32)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^{15}ln(8x^8)

\int x^{15} ln (8 x^{8}) d x

\frac{1}{16} x^{16} (3 ln (2) + 8 ln (x)) - \frac{x ^{16}}{32} + C

Solution steps

\int x^{15} ln (8 x^{8}) d x

Apply Integration By Parts

: \frac{1}{16} x^{16} ln (8 x^{8}) - \int \frac{x ^{15}}{2} d x

= \frac{1}{16} x^{16} ln (8 x^{8}) - \int \frac{x ^{15}}{2} d x

\int \frac{x ^{15}}{2} d x = \frac{x ^{16}}{32}

= \frac{1}{16} x^{16} ln (8 x^{8}) - \frac{x ^{16}}{32}

\frac{1}{16} x^{16} ln (8 x^{8}) = \frac{1}{16} x^{16} (3 ln (2) + 8 ln (x))

= \frac{1}{16} x^{16} (3 ln (2) + 8 ln (x)) - \frac{x ^{16}}{32}

Add a constant to the solution

= \frac{1}{16} x^{16} (3 ln (2) + 8 ln (x)) - \frac{x ^{16}}{32} + C

\int \frac{1}{x ^{3} y ^{2}} d x

\int (x^{3} + 2)^{2} \cdot 3 x^{2} d x

\int 2 3 x d x

\int - cos (x) + 2 d x

\int \frac{1}{4 + cos ( x )} d x

What is the integral of x^{15}ln(8x^8) ?
The integral of x^{15}ln(8x^8) is 1/16 x^{16}(3ln(2)+8ln(x))-(x^{16})/(32)+C