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Popular >

integral of (x+1)2

Solution

\int (x + 1) 2 d x

Solution

x^{2} + 2 x + C

Solution steps

\int (x + 1) \cdot 2 d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int 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

= 2 (\int x d x + \int 1 d x)

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

\int 1 d x = x

= 2 (\frac{x ^{2}}{2} + x)

Simplify

2 (\frac{x ^{2}}{2} + x) : x^{2} + 2 x

= x^{2} + 2 x

Add a constant to the solution

= x^{2} + 2 x + C

Popular Examples

y^{^{'}} - 4 y = 2 x y^{2}

derivative of ((x+3)/(x-3))

\frac{d}{d x} (\frac{( x + 3 )}{x - 3})

derivative of x/(x+25)derivative of

\frac{x}{x + 25}

y^{''}+2y^'+5y=x

y^{^{''}} + 2 y^{^{'}} + 5 y = x

integral of 5/((x^2-1)^2)

\int \frac{5}{( x ^{2} - 1 ) ^{2}} d x

Frequently Asked Questions (FAQ)

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