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Popular >

integral of (x+1)^2

Solution

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

Solution

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

Solution steps

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

Expand

(x + 1)^{2} : x^{2} + 2 x + 1

= \int x^{2} + 2 x + 1 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 2 x d x + \int 1 d x

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

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

\int 1 d x = x

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

Add a constant to the solution

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

Popular Examples

integral of cosh(mt)

\int cosh (m t) d t

integral from-2 to 5 of 6

\int_{- 2}^{5} 6 d x

y^{^{''}} - 3 y^{^{'}} = 9 t

y^'-4/x y=((y^4))/(x^9)

y^{^{'}} - \frac{4}{x} y = \frac{( y ^{4} )}{x ^{9}}

integral of 3x^2+sqrt(3)

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

Frequently Asked Questions (FAQ)

What is the integral of (x+1)^2 ?
The integral of (x+1)^2 is (x^3)/3+x^2+x+C