What is the integral of 2/(x^3)+3/(x^2)+5 ?

The integral of 2/(x^3)+3/(x^2)+5 is -1/(x^2)-3/x+5x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2/(x^3)+3/(x^2)+5

\int \frac{2}{x ^{3}} + \frac{3}{x ^{2}} + 5 d x

- \frac{1}{x ^{2}} - \frac{3}{x} + 5 x + C

Solution steps

\int \frac{2}{x ^{3}} + \frac{3}{x ^{2}} + 5 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{2}{x ^{3}} d x + \int \frac{3}{x ^{2}} d x + \int 5 d x

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

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

\int 5 d x = 5 x

= - \frac{1}{x ^{2}} - \frac{3}{x} + 5 x

Add a constant to the solution

= - \frac{1}{x ^{2}} - \frac{3}{x} + 5 x + C

x^{^{''}} + x^{^{'}} = 0

x^{2} arctan (5 x)

\int e^{\frac{4 x}{9}} (\frac{4}{9}) d x

x^{2} - 4 x

\frac{d}{d x} (lo g_{10} (7 x))

What is the integral of 2/(x^3)+3/(x^2)+5 ?
The integral of 2/(x^3)+3/(x^2)+5 is -1/(x^2)-3/x+5x+C