What is the integral of (x^2-5x+7) ?

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

\int (x^{2} - 5 x + 7) d x

\frac{x ^{3}}{3} - \frac{5 x ^{2}}{2} + 7 x + C

Solution steps

\int x^{2} - 5 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 x^{2} d x - \int 5 x d x + \int 7 d x

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

\int 5 x d x = \frac{5 x ^{2}}{2}

\int 7 d x = 7 x

= \frac{x ^{3}}{3} - \frac{5 x ^{2}}{2} + 7 x

Add a constant to the solution

= \frac{x ^{3}}{3} - \frac{5 x ^{2}}{2} + 7 x + C

\int sin (25 t) sec^{2} (cos (25 t)) d t

\int \frac{1 - sin ( t )}{t + cos ( t )} d t

\int \frac{1}{( 5 t + 1 ) ^{2} - 1} d t

\int \frac{x ^{5} - 1}{x - 1} d x

\int \frac{1 - ln ( x )}{x ln ( x )} d x

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