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Popular >

integral of x^2+2x+3

Solution

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

Solution

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

Solution steps

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

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

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

\int 3 d x = 3 x

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

Add a constant to the solution

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

Popular Examples

derivative of (x^2+y^2^6)

\frac{d}{d x} ((x^{2} + y^{2})^{6})

(\partial}{\partial v}(\frac{u+v)/2)

\frac{\partial}{\partial v} (\frac{u + v}{2})

y^{''''}-9y^{''}+20y=0

y^{^{''''}} - 9 y^{^{''}} + 20 y = 0

integral of (10\sqrt[3]{5x-2})/3

integral from 0 to 3 of sqrt(1+16x^2)

\int_{0}^{3} 1 + 16 x^{2} d x

Frequently Asked Questions (FAQ)

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