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

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

Popular >

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

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

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

Solution steps

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

\int 2 d x = 2 x

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

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

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

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{x + 5}{x - 3})

\frac{d}{d y} (y^{\frac{4}{5}})

y^{^{'}} = y (x y^{4} + 5)

\int_{1}^{7} (x^{2} - 4 x - 12) d x

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

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