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Popular >

integral of x(x^2+4)

Solution

\int x (x^{2} + 4) d x

Solution

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

Solution steps

\int x (x^{2} + 4) d x

Expand

x (x^{2} + 4) : x^{3} + 4 x

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

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

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

= \frac{x ^{4}}{4} + 2 x^{2}

Add a constant to the solution

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

Graph

Popular Examples

integral of 3x^2+5

\int 3 x^{2} + 5 d x

(dv}{dt}=\frac{49-10v)/5

\frac{d v}{d t} = \frac{49 - 10 v}{5}

(dy)/(dx)=y(y-1)

\frac{d y}{d x} = y (y - 1)

area y=x,y=3x,y=-x+4 area

y = x, y = 3 x, y = - x + 4

(y+sqrt(xy))dx=xdy

(y + x y) d x = x d y

Frequently Asked Questions (FAQ)

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