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Popular >

integral of x^2-3x+7

Solution

\int x^{2} - 3 x + 7 d x

Solution

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

Solution steps

\int x^{2} - 3 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 3 x d x + \int 7 d x

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

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

\int 7 d x = 7 x

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

Add a constant to the solution

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

Popular Examples

derivative of 2/3 x^6 derivative of

\frac{2}{3} x^{6}

integral from 7 to 8 of 1/((x-7)^{3/2)}

\int_{7}^{8} \frac{1}{( x - 7 ) ^{\frac{3}{2}}} d x

(x+1)((dy)/(dx))=(x+6)

(x + 1) (\frac{d y}{d x}) = (x + 6)

limit as x approaches 0 of x^{-8}

x \to 0 lim (x^{- 8})

integral of sin(5x-1)

\int sin (5 x - 1) d x

Frequently Asked Questions (FAQ)

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