What is the integral of x^4+2x^2+1 ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^4+2x^2+1

\int x^{4} + 2 x^{2} + 1 d x

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

Solution steps

\int x^{4} + 2 x^{2} + 1 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^{4} d x + \int 2 x^{2} d x + \int 1 d x

\int x^{4} d x = \frac{x ^{5}}{5}

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

\int 1 d x = x

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

Add a constant to the solution

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

\int sin^{2} (2 x) \cdot cos (2 x) d x

f (x) = \frac{1}{x}, at x = 1.003

x^{5} e^{2 x}

\frac{\partial}{\partial x} (e^{- 3 π t} cos (4 x) sin (6 y))

y = in (x)

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