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Popular >

integral of x^2-5x+5

Solution

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

Solution

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

Solution steps

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

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

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

\int 5 d x = 5 x

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

Add a constant to the solution

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

Popular Examples

integral of x^2(x^3+1)^{10}

\int x^{2} (x^{3} + 1)^{10} d x

integral from pi/2 to pi of 4cot(x/2)

\int_{\frac{π}{2}}^{π} 4 cot (\frac{x}{2}) d x

derivative of 2x^3+x

\frac{d}{d x} (2 x^{3} + x)

(\partial)/(\partial x)(y^2e^{2x})

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

derivative of e^{x^2-4}+2x+9

\frac{d}{d x} (e^{x^{2} - 4} + 2 x + 9)

Frequently Asked Questions (FAQ)

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