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Popular >

integral of x^2+x+1

Solution

integral

x^{2} + x + 1

Solution

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

Solution steps

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

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

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

\int 1 d x = x

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

Add a constant to the solution

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

Popular Examples

integral of (-x^2)/(2(1-x^2)^2)

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

integral of 1/(sqrt(\sqrt{x)-1)}

\int \frac{1}{x - 1} d x

integral of-3(x+2)^{-2}

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

integral of ((x^2-3x+5)/(sqrt(x)))

\int (\frac{x ^{2} - 3 x + 5}{x}) d x

integral of ln(2x) 1/x

\int ln (2 x) \frac{1}{x} d x

Frequently Asked Questions (FAQ)

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