What is the integral of (x^2+2/(x^3)-7) ?

The integral of (x^2+2/(x^3)-7) is (x^3)/3-1/(x^2)-7x+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+2/(x^3)-7)

\int (x^{2} + \frac{2}{x ^{3}} - 7) d x

\frac{x ^{3}}{3} - \frac{1}{x ^{2}} - 7 x + C

Solution steps

\int x^{2} + \frac{2}{x ^{3}} - 7 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{2}{x ^{3}} d x - \int 7 d x

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

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

\int 7 d x = 7 x

= \frac{x ^{3}}{3} - \frac{1}{x ^{2}} - 7 x

Add a constant to the solution

= \frac{x ^{3}}{3} - \frac{1}{x ^{2}} - 7 x + C

\int x \frac{1}{4} d x

\int x 3 a + x d x

\int t^{2} - 6 t d t

\int (2 x^{5}) e^{x} d x

\int x (x + 1) (2 x - 1) d x

What is the integral of (x^2+2/(x^3)-7) ?
The integral of (x^2+2/(x^3)-7) is (x^3)/3-1/(x^2)-7x+C