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Popular >

integral of x^2+4x

Solution

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

Solution

\frac{x ^{3}}{3} + 2 x^{2} + C

Solution steps

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

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

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

= \frac{x ^{3}}{3} + 2 x^{2}

Add a constant to the solution

= \frac{x ^{3}}{3} + 2 x^{2} + C

Popular Examples

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

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

d/(dy)(arctan(x/y))

\frac{d}{d y} (arctan (\frac{x}{y}))

derivative of x/((1+4x^2))

\frac{d}{d x} (\frac{x}{( 1 + 4 x ) ^{2}})

integral of (12)/(4x^2+5x+1)

\int \frac{12}{4 x ^{2} + 5 x + 1} d x

integral of (x+3)^2(3-x)^7

\int (x + 3)^{2} (3 - x)^{7} d x

Frequently Asked Questions (FAQ)

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