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Popular >

integral of 6x^2-x^3

Solution

\int 6 x^{2} - x^{3} d x

Solution

2 x^{3} - \frac{x ^{4}}{4} + C

Solution steps

\int 6 x^{2} - 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 6 x^{2} d x - \int x^{3} d x

\int 6 x^{2} d x = 2 x^{3}

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

= 2 x^{3} - \frac{x ^{4}}{4}

Add a constant to the solution

= 2 x^{3} - \frac{x ^{4}}{4} + C

Popular Examples

integral of (cos(x))/(4+sin(x))

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

integral of (2-5x)/(x^6)

\int \frac{2 - 5 x}{x ^{6}} d x

(dy)/(dx)+(2xy)/(x^2+1)=x

\frac{d y}{d x} + \frac{2 x y}{x ^{2} + 1} = x

tangent of 3/(x^2)tangent of

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

integral of 1/(x^2sqrt(x^2+9))

\int \frac{1}{x ^{2} x ^{2} + 9} d x

Frequently Asked Questions (FAQ)

What is the integral of 6x^2-x^3 ?
The integral of 6x^2-x^3 is 2x^3-(x^4)/4+C