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Popular >

integral of-x^3+9x

Solution

\int - x^{3} + 9 x d x

Solution

- \frac{x ^{4}}{4} + \frac{9 x ^{2}}{2} + C

Solution steps

\int - x^{3} + 9 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 x^{3} d x + \int 9 x d x

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

\int 9 x d x = \frac{9 x ^{2}}{2}

= - \frac{x ^{4}}{4} + \frac{9 x ^{2}}{2}

Add a constant to the solution

= - \frac{x ^{4}}{4} + \frac{9 x ^{2}}{2} + C

Popular Examples

integral of 2/((t-9)^2)

\int \frac{2}{( t - 9 ) ^{2}} d t

integral of 6x^2+2x

\int 6 x^{2} + 2 x d x

integral of x^{-3}cos(1/x)

\int x^{- 3} cos (\frac{1}{x}) d x

integral of e^{1/(4x)}

\int e^{\frac{1}{4 x}} d x

integral of (u^6-2u^5-u^3+2/7)

\int (u^{6} - 2 u^{5} - u^{3} + \frac{2}{7}) d u

Frequently Asked Questions (FAQ)

What is the integral of-x^3+9x ?
The integral of-x^3+9x is -(x^4)/4+(9x^2)/2+C