What is the integral of (2x^3-5x^2-8x+15)/(x-3) ?

The integral of (2x^3-5x^2-8x+15)/(x-3) is (2x^3)/3+(x^2)/2-5x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2x^3-5x^2-8x+15)/(x-3)

\int \frac{2 x ^{3} - 5 x ^{2} - 8 x + 15}{x - 3} d x

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

Solution steps

\int \frac{2 x ^{3} - 5 x ^{2} - 8 x + 15}{x - 3} d x

Simplify

\frac{2 x ^{3} - 5 x ^{2} - 8 x + 15}{x - 3} : 2 x^{2} + x - 5

= \int 2 x^{2} + x - 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 2 x^{2} d x + \int x d x - \int 5 d x

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

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

\int 5 d x = 5 x

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

Add a constant to the solution

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

\int 7 - sin (x) d x

\int tan (2 x) sin (2 x) d x

\int \frac{5 x ^{3} - 3 x ^{2} + 4 x - 3}{x ^{4} + x ^{2}} d x

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

\int \frac{cos ( t )}{sin ^{7} ( t )} d t

What is the integral of (2x^3-5x^2-8x+15)/(x-3) ?
The integral of (2x^3-5x^2-8x+15)/(x-3) is (2x^3)/3+(x^2)/2-5x+C