What is the integral of (x^2+1/((3x)^2)) ?

The integral of (x^2+1/((3x)^2)) is (x^3)/3-1/(9x)+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+1/((3x)^2))

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

\frac{x ^{3}}{3} - \frac{1}{9 x} + C

Solution steps

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

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

\int \frac{1}{( 3 x ) ^{2}} d x = - \frac{1}{9 x}

= \frac{x ^{3}}{3} - \frac{1}{9 x}

Add a constant to the solution

= \frac{x ^{3}}{3} - \frac{1}{9 x} + C

\int x^{3} - 3 x^{2} + 2 x d x

\int \frac{x ^{3} - 6 x ^{2} + 11 x - 6}{4 x ^{3} - 28 x ^{2} + 56 x - 32} d x

\int_{- \infty}^{0} e^{5 x} d x

\frac{\partial}{\partial x} (5 x ln (x^{2} + y))

x \to 0 lim (x^{2} - 6)

What is the integral of (x^2+1/((3x)^2)) ?
The integral of (x^2+1/((3x)^2)) is (x^3)/3-1/(9x)+C