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Popular >

integral of 9x-x^3

Solution

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

Solution

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

Solution steps

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

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

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

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

Add a constant to the solution

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

Popular Examples

integral of (20y^3)/(5y^4+1)

\int \frac{20 y ^{3}}{5 y ^{4} + 1} d y

integral of ((4+sqrt(x)+x)/x)

\int (\frac{4 + x + x}{x}) d x

integral of (x+25)^{-2}

\int (x + 25)^{- 2} d x

integral of (4x^3-12x)(x^4-6x^2)^{-3}

\int (4 x^{3} - 12 x) (x^{4} - 6 x^{2})^{- 3} d x

integral of (x^4+2x^2-x+9)/(x^5+2x^4)

\int \frac{x ^{4} + 2 x ^{2} - x + 9}{x ^{5} + 2 x ^{4}} d x

Frequently Asked Questions (FAQ)

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