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Popular >

integral of 5x^2+x

Solution

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

Solution

\frac{5 x ^{3}}{3} + \frac{x ^{2}}{2} + C

Solution steps

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

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

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

= \frac{5 x ^{3}}{3} + \frac{x ^{2}}{2}

Add a constant to the solution

= \frac{5 x ^{3}}{3} + \frac{x ^{2}}{2} + C

Popular Examples

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

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

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

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

integral of (7sqrt(x^3)+6\sqrt[3]{x^2})

integral of cos(10x+2)cos(8x-2)

\int cos (10 x + 2) cos (8 x - 2) d x

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

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

Frequently Asked Questions (FAQ)

What is the integral of 5x^2+x ?
The integral of 5x^2+x is (5x^3)/3+(x^2)/2+C