What is the integral of (x^2-4x+5) ?

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

\int (x^{2} - 4 x + 5) d x

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

Solution steps

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

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

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

\int 5 d x = 5 x

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

Add a constant to the solution

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

4 + 3 x

\frac{d}{d x} (arcsin (\frac{x}{10}))

\frac{\partial}{\partial x} (- \frac{4}{x ^{2} y})

x^{^{''}} - 20 x^{^{'}} + 91 x = 0

f (t) = t^{\frac{1}{2}} (13 t + 2)

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