What is the integral of x^2+ln(x) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^2+ln(x)

\int x^{2} + ln (x) d x

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

Solution steps

\int x^{2} + ln (x) 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 x^{2} d x + \int ln (x) d x

\int x^{2} d x = \frac{x ^{3}}{3}

\int ln (x) d x = x ln (x) - x

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

Add a constant to the solution

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

\int x^{3} + 4 x d x

\int sin^{3} (5 θ) cos (5 θ) d θ

\int \frac{1}{4 x ^{2} + 25} d x

\int \frac{2 x ^{6} - 3 x ^{4} - x ^{3}}{x ^{3}} d x

\int (- 9 + \frac{8}{p}) d p

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