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

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

Popular >

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

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

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

Solution steps

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

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

\int 1 d u = u

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

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

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

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

Add a constant to the solution

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

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

\int 2 e^{t} - 3 cos (t) d t

\int x (3 x^{2} + 1)^{4} d x

\int (\frac{1}{x} + \frac{1}{x ln ( x )}) d x

\int - \frac{cos ( 4 x )}{4} d x

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