What is the integral of (1+x+x^2+x^3) ?

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

integral of (1+x+x^2+x^3)

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

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

Solution steps

\int 1 + x + x^{2} + x^{3} 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 1 d x + \int x d x + \int x^{2} d x + \int x^{3} d x

\int 1 d x = x

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

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

\int x^{3} d x = \frac{x ^{4}}{4}

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

Add a constant to the solution

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

\int \frac{( 5 x ^{2} - 12 )}{( x ^{2} - 6 x + 13 ) ^{2}} d x

n = 1 \sum \infty \frac{1}{1 + n}

\frac{d}{d y} (y^{2} + 1)

x \to 3 lim (\frac{2}{3 - 2})

\frac{d}{d x} f (x) = x^{\frac{- 11}{12}}

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