What is the integral of (2x^5+3x^4+6x^3-7x^2)/(x^2) ?

The integral of (2x^5+3x^4+6x^3-7x^2)/(x^2) is (x^4)/2+x^3+3x^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 (2x^5+3x^4+6x^3-7x^2)/(x^2)

\int \frac{2 x ^{5} + 3 x ^{4} + 6 x ^{3} - 7 x ^{2}}{x ^{2}} d x

\frac{x ^{4}}{2} + x^{3} + 3 x^{2} - 7 x + C

Solution steps

\int \frac{2 x ^{5} + 3 x ^{4} + 6 x ^{3} - 7 x ^{2}}{x ^{2}} d x

Simplify

\frac{2 x ^{5} + 3 x ^{4} + 6 x ^{3} - 7 x ^{2}}{x ^{2}} : 2 x^{3} + 3 x^{2} + 6 x - 7

= \int 2 x^{3} + 3 x^{2} + 6 x - 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 2 x^{3} d x + \int 3 x^{2} d x + \int 6 x d x - \int 7 d x

\int 2 x^{3} d x = \frac{x ^{4}}{2}

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

\int 6 x d x = 3 x^{2}

\int 7 d x = 7 x

= \frac{x ^{4}}{2} + x^{3} + 3 x^{2} - 7 x

Add a constant to the solution

= \frac{x ^{4}}{2} + x^{3} + 3 x^{2} - 7 x + C

\int x 196 - 49 x^{2} d x

\int \frac{( 2 x + 8 )}{( x ^{2} + 2 x + 5 ) ^{2}} d x

\int \frac{7 x + x ^{2}}{( x - 4 ) ( 2 x + 3 ) ( 2 x + 1 )} d x

\int ln (x + 17) d x

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

What is the integral of (2x^5+3x^4+6x^3-7x^2)/(x^2) ?
The integral of (2x^5+3x^4+6x^3-7x^2)/(x^2) is (x^4)/2+x^3+3x^2-7x+C