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Popular >

integral of (x+6)^2

Solution

\int (x + 6)^{2} d x

Solution

\frac{x ^{3}}{3} + 6 x^{2} + 36 x + C

Solution steps

\int (x + 6)^{2} d x

Expand

(x + 6)^{2} : x^{2} + 12 x + 36

= \int x^{2} + 12 x + 36 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 12 x d x + \int 36 d x

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

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

\int 36 d x = 36 x

= \frac{x ^{3}}{3} + 6 x^{2} + 36 x

Add a constant to the solution

= \frac{x ^{3}}{3} + 6 x^{2} + 36 x + C

Popular Examples

integral of sin(x)*sin(2*x)

\int sin (x) \cdot sin (2 \cdot x) d x

derivative of (x-sqrt(x))/(x^{1/4)}derivative of

\frac{x - x}{x ^{\frac{1}{4}}}

derivative of 5/2 x^{5/2}derivative of

\frac{5}{2} x^{\frac{5}{2}}

tangent of f(x)=2x^4-10x^2,\at x=-2 tangent of

f (x) = 2 x^{4} - 10 x^{2}, at x = - 2

derivative of ln(x-pi/2)

\frac{d}{d x} (ln (x - \frac{π}{2}))

Frequently Asked Questions (FAQ)

What is the integral of (x+6)^2 ?
The integral of (x+6)^2 is (x^3)/3+6x^2+36x+C