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Popular >

integral of (3-x^2)3

Solution

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

Solution

9 x - x^{3} + C

Solution steps

\int (3 - x^{2}) \cdot 3 d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int 3 - x^{2} 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

= 3 (\int 3 d x - \int x^{2} d x)

\int 3 d x = 3 x

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

= 3 (3 x - \frac{x ^{3}}{3})

Simplify

3 (3 x - \frac{x ^{3}}{3}) : 9 x - x^{3}

= 9 x - x^{3}

Add a constant to the solution

= 9 x - x^{3} + C

Popular Examples

(dy)/(dx)=(1/(sec^2(y)))

\frac{d y}{d x} = (\frac{1}{sec ^{2} ( y )})

laplacetransform sin(t+pi/3)laplace transform

sin (t + \frac{π}{3})

derivative of f(x)=-3 derivative of

f (x) = - 3

integral from-2 to 1 of x

\int_{- 2}^{1} x d x

(dy)/(dx)=e^{2x+5y}

\frac{d y}{d x} = e^{2 x + 5 y}

Frequently Asked Questions (FAQ)

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