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Popular >

integral of (x+7)^2

Solution

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

Solution

\frac{x ^{3}}{3} + 7 x^{2} + 49 x + C

Solution steps

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

Expand

(x + 7)^{2} : x^{2} + 14 x + 49

= \int x^{2} + 14 x + 49 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 14 x d x + \int 49 d x

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

\int 14 x d x = 7 x^{2}

\int 49 d x = 49 x

= \frac{x ^{3}}{3} + 7 x^{2} + 49 x

Add a constant to the solution

= \frac{x ^{3}}{3} + 7 x^{2} + 49 x + C

Popular Examples

integral of (x^2)/(sqrt(2+x^3))

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

area x,(x^2)/4 ,0,2 area

x, \frac{x ^{2}}{4}, 0, 2

2y^{'''}+3y^{''}-11y^'-6y=0

2 y^{^{'''}} + 3 y^{^{''}} - 11 y^{^{'}} - 6 y = 0

integral of (24)/((144x^2+1)^2)

\int \frac{24}{( 144 x ^{2} + 1 ) ^{2}} d x

integral from 0 to 9 of e^xsin(x)

\int_{0}^{9} e^{x} sin (x) d x

Frequently Asked Questions (FAQ)

What is the integral of (x+7)^2 ?
The integral of (x+7)^2 is (x^3)/3+7x^2+49x+C