What is the integral of x^7ln(x^4) ?

The integral of x^7ln(x^4) is 4(1/8 x^8ln(x)-(x^8)/(64))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^7ln(x^4)

\int x^{7} ln (x^{4}) d x

4 (\frac{1}{8} x^{8} ln (x) - \frac{x ^{8}}{64}) + C

Solution steps

\int x^{7} ln (x^{4}) d x

Simplify

ln (x^{4}) : 4 ln (x)

= \int 4 x^{7} ln (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 4 \cdot \int x^{7} ln (x) d x

Apply Integration By Parts

: \frac{1}{8} x^{8} ln (x) - \int \frac{x ^{7}}{8} d x

= 4 (\frac{1}{8} x^{8} ln (x) - \int \frac{x ^{7}}{8} d x)

\int \frac{x ^{7}}{8} d x = \frac{x ^{8}}{64}

= 4 (\frac{1}{8} x^{8} ln (x) - \frac{x ^{8}}{64})

Add a constant to the solution

= 4 (\frac{1}{8} x^{8} ln (x) - \frac{x ^{8}}{64}) + C

\int 16 cos (4 x) d x

\int \frac{- 8}{x} d x

\int \frac{x ^{4}}{e ^{x^{5}}} d x

\int 6 e^{2 x + 1} d x

\int 9 cos^{2} (t) d t

What is the integral of x^7ln(x^4) ?
The integral of x^7ln(x^4) is 4(1/8 x^8ln(x)-(x^8)/(64))+C