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Popular >

integral of 3x^2-x^3

Solution

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

Solution

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

Solution steps

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

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

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

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

Add a constant to the solution

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

Popular Examples

limit as x approaches 1 of sqrt(x+8)

x \to 1 lim (x + 8)

integral of sec^2(x)tan^9(x)

\int sec^{2} (x) tan^{9} (x) d x

(d^2)/(dx^2)((x^3)/(x^2-1))

\frac{d ^{2}}{d x ^{2}} (\frac{x ^{3}}{x ^{2} - 1})

sum from n=1 to infinity of 1/(3^n-5)

n = 1 \sum \infty \frac{1}{3 ^{n} - 5}

derivative of 2+3/(1+(x+1)^2)derivative of

2 + \frac{3}{1 + ( x + 1 ) ^{2}}

Frequently Asked Questions (FAQ)

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