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Popular >

integral of 4x^2-x^4

Solution

\int 4 x^{2} - x^{4} d x

Solution

\frac{4 x ^{3}}{3} - \frac{x ^{5}}{5} + C

Solution steps

\int 4 x^{2} - x^{4} 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 x^{2} d x - \int x^{4} d x

\int 4 x^{2} d x = \frac{4 x ^{3}}{3}

\int x^{4} d x = \frac{x ^{5}}{5}

= \frac{4 x ^{3}}{3} - \frac{x ^{5}}{5}

Add a constant to the solution

= \frac{4 x ^{3}}{3} - \frac{x ^{5}}{5} + C

Graph

Popular Examples

limit as x approaches-1+of x+2

x \to - 1 + lim (x + 2)

(dx)/(dt)=8(x^2+1),x(pi/4)=1

\frac{d x}{d t} = 8 (x^{2} + 1), x (\frac{π}{4}) = 1

derivative of (-1/((x-1)^2))

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

(dy)/(dt)-2ty=12t^2e^{t^2}

\frac{d y}{d t} - 2 t y = 12 t^{2} e^{t^{2}}

y^'=(2y^2)+xy^2

y^{^{'}} = (2 y^{2}) + x y^{2}

Frequently Asked Questions (FAQ)

What is the integral of 4x^2-x^4 ?
The integral of 4x^2-x^4 is (4x^3)/3-(x^5)/5+C