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Popular >

integral of x^2-5x+7

Solution

\int x^{2} - 5 x + 7 d x

Solution

\frac{x ^{3}}{3} - \frac{5 x ^{2}}{2} + 7 x + C

Solution steps

\int x^{2} - 5 x + 7 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 7 d x

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

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

\int 7 d x = 7 x

= \frac{x ^{3}}{3} - \frac{5 x ^{2}}{2} + 7 x

Add a constant to the solution

= \frac{x ^{3}}{3} - \frac{5 x ^{2}}{2} + 7 x + C

Popular Examples

integral of e^{-u^2}

\int e^{- u^{2}} d u

sum from n=1 to infinity of (7/8)^{n-1}

n = 1 \sum \infty (\frac{7}{8})^{n - 1}

derivative of e^{x/(x-8})

\frac{d}{d x} (e^{\frac{x}{x - 8}})

integral of (9x^2-8x)e^{2x}

\int (9 x^{2} - 8 x) e^{2 x} d x

y^{^{''}} - 6 y + 9 y = 0

Frequently Asked Questions (FAQ)

What is the integral of x^2-5x+7 ?
The integral of x^2-5x+7 is (x^3)/3-(5x^2)/2+7x+C