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Popular >

integral of (2-3x)^2

Solution

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

Solution

4 x - 6 x^{2} + 3 x^{3} + C

Solution steps

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

Expand

(2 - 3 x)^{2} : 4 - 12 x + 9 x^{2}

= \int 4 - 12 x + 9 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

= \int 4 d x - \int 12 x d x + \int 9 x^{2} d x

\int 4 d x = 4 x

\int 12 x d x = 6 x^{2}

\int 9 x^{2} d x = 3 x^{3}

= 4 x - 6 x^{2} + 3 x^{3}

Add a constant to the solution

= 4 x - 6 x^{2} + 3 x^{3} + C

Popular Examples

ydx=(ye^{y-2x})dy

y d x = (y e^{y - 2 x}) d y

derivative of f(x)=sqrt(6-7x)derivative of

f (x) = 6 - 7 x

limit as x approaches infinity of (5x+6x^2)/(3x-8)

x \to \infty lim (\frac{5 x + 6 x ^{2}}{3 x - 8})

laplacetransform 1/2 laplace transform

\frac{1}{2}

limit as x approaches 5 of ((x^4-625))/(x-5)

x \to 5 lim (\frac{( x ^{4} - 625 )}{x - 5})

Frequently Asked Questions (FAQ)

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