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Popular >

integral of (2x+4)^2

Solution

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

Solution

\frac{4 x ^{3}}{3} + 8 x^{2} + 16 x + C

Solution steps

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

Expand

(2 x + 4)^{2} : 4 x^{2} + 16 x + 16

= \int 4 x^{2} + 16 x + 16 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 16 x d x + \int 16 d x

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

\int 16 x d x = 8 x^{2}

\int 16 d x = 16 x

= \frac{4 x ^{3}}{3} + 8 x^{2} + 16 x

Add a constant to the solution

= \frac{4 x ^{3}}{3} + 8 x^{2} + 16 x + C

Popular Examples

derivative of 1/(ln(2))

\frac{d}{d x} (\frac{1}{ln ( 2 )})

tangent of y=(7x)/(x-1),(2,14)tangent of

y = \frac{7 x}{x - 1}, (2, 14)

(\partial)/(\partial x)((x+2)^2*(1+1/y)^3)

\frac{\partial}{\partial x} ((x + 2)^{2} \cdot (1 + \frac{1}{y})^{3})

derivative of y=sqrt(x^2+11)derivative of

y = x^{2} + 11

(\partial)/(\partial z)(x-z)

\frac{\partial}{\partial z} (x - z)

Frequently Asked Questions (FAQ)

What is the integral of (2x+4)^2 ?
The integral of (2x+4)^2 is (4x^3)/3+8x^2+16x+C