What is the integral of 5-(x-1)^2 ?

The integral of 5-(x-1)^2 is -(x^3)/3+x^2+4x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 5-(x-1)^2

\int 5 - (x - 1)^{2} d x

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

Solution steps

\int 5 - (x - 1)^{2} 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 5 d x - \int (x - 1)^{2} d x

\int 5 d x = 5 x

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

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

Simplify

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

Add a constant to the solution

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

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

\int (\frac{y ^{3} - 1}{y})^{2} d y

\int 5 x sin (3 x) d x

\int \frac{cos ( x )}{1 - ( cos ( x ) ) ^{2}} d x

\int 4 x (1 - x^{2}) d x

What is the integral of 5-(x-1)^2 ?
The integral of 5-(x-1)^2 is -(x^3)/3+x^2+4x+C