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

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

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

\frac{x ^{6}}{6} - x^{2} + 4 x + C

Solution steps

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

\int x^{5} d x = \frac{x ^{6}}{6}

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

\int 4 d x = 4 x

= \frac{x ^{6}}{6} - x^{2} + 4 x

Add a constant to the solution

= \frac{x ^{6}}{6} - x^{2} + 4 x + C

y = \frac{10 x + 15}{x}

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 4 y = 0

y^{^{'}} = - 3 y + e^{- 2 x}

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

\int_{- 2}^{- 1} \frac{1}{x} d x

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