What is the integral of ((ln(x))^3)/3-2 ?

The integral of ((ln(x))^3)/3-2 is 1/3 xln^3(x)-xln^2(x)+2xln(x)-4x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ((ln(x))^3)/3-2

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

\frac{1}{3} x ln^{3} (x) - x ln^{2} (x) + 2 x ln (x) - 4 x + C

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{( ln ( x ) ) ^{3}}{3} d x - \int 2 d x

\int \frac{( ln ( x ) ) ^{3}}{3} d x = \frac{1}{3} x ln^{3} (x) - x ln^{2} (x) + 2 x ln (x) - 2 x

\int 2 d x = 2 x

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

Simplify

= \frac{1}{3} x ln^{3} (x) - x ln^{2} (x) + 2 x ln (x) - 4 x

Add a constant to the solution

= \frac{1}{3} x ln^{3} (x) - x ln^{2} (x) + 2 x ln (x) - 4 x + C

\int (\frac{5}{1 - x ^{2}} + \frac{3}{x}) d x

\int \frac{x ^{2} + 10 x - 36}{x ( x - 3 ) ^{2}} d x

\int - 5 d x

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

\int 4 e^{0.8 x} - 0.5 y d x

What is the integral of ((ln(x))^3)/3-2 ?
The integral of ((ln(x))^3)/3-2 is 1/3 xln^3(x)-xln^2(x)+2xln(x)-4x+C