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Popular >

integral of 2x+x^2

Solution

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

Solution

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

Solution steps

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

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

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

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

Add a constant to the solution

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

Popular Examples

integral of 4x^4e^{2x^5}

\int 4 x^{4} e^{2 x^{5}} d x

integral of 25x^2(125x^3+1)^{12}

\int 25 x^{2} (125 x^{3} + 1)^{12} d x

integral of x/(1+5x^2)

\int \frac{x}{1 + 5 x ^{2}} d x

integral of x^2(5x^3-2)

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

integral of 6x^3(-7-3x^4)^2

\int 6 x^{3} (- 7 - 3 x^{4})^{2} d x

Frequently Asked Questions (FAQ)

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