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Popular >

integral of-x^2+5x-4

Solution

\int - x^{2} + 5 x - 4 d x

Solution

- \frac{x ^{3}}{3} + \frac{5 x ^{2}}{2} - 4 x + C

Solution steps

\int - x^{2} + 5 x - 4 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 4 d x

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

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

\int 4 d x = 4 x

= - \frac{x ^{3}}{3} + \frac{5 x ^{2}}{2} - 4 x

Add a constant to the solution

= - \frac{x ^{3}}{3} + \frac{5 x ^{2}}{2} - 4 x + C

Popular Examples

x*(dy)/(dx)+y= 1/(y^2)

x \cdot \frac{d y}{d x} + y = \frac{1}{y ^{2}}

integral from 0 to e of x^2ln(x)

\int_{0}^{e} x^{2} ln (x) d x

derivative of ln(x+e^x)

\frac{d}{d x} (ln (x + e^{x}))

y^'=((1-y)^5)/4

y^{^{'}} = \frac{( 1 - y ) ^{5}}{4}

derivative of y=2xe^{-x}+2e^{x^5}derivative of

y = 2 x e^{- x} + 2 e^{x^{5}}

Frequently Asked Questions (FAQ)

What is the integral of-x^2+5x-4 ?
The integral of-x^2+5x-4 is -(x^3)/3+(5x^2)/2-4x+C