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Popular >

integral of x^2+5x

Solution

\int x^{2} + 5 x d x

Solution

\frac{x ^{3}}{3} + \frac{5 x ^{2}}{2} + C

Solution steps

\int x^{2} + 5 x 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 5 x d x

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

\int 5 x d x = \frac{5 x ^{2}}{2}

= \frac{x ^{3}}{3} + \frac{5 x ^{2}}{2}

Add a constant to the solution

= \frac{x ^{3}}{3} + \frac{5 x ^{2}}{2} + C

Graph

Popular Examples

(\partial)/(\partial x)(5x^4+x^3y+xy+y^4)

\frac{\partial}{\partial x} (5 x^{4} + x^{3} y + x y + y^{4})

(\partial)/(\partial y)(4xy^2)

\frac{\partial}{\partial y} (4 x y^{2})

limit as x approaches infinity of 2/x

x \to \infty lim (\frac{2}{x})

-6t^2y^{''}+3t(t+4)y^'-3(t+4)y=4t^3

- 6 t^{2} y^{^{''}} + 3 t (t + 4) y^{^{'}} - 3 (t + 4) y = 4 t^{3}

(dy)/(dx)+e^xy^2=x^2y^2

\frac{d y}{d x} + e^{x} y^{2} = x^{2} y^{2}

Frequently Asked Questions (FAQ)

What is the integral of x^2+5x ?
The integral of x^2+5x is (x^3)/3+(5x^2)/2+C