What is the integral of f(x)=5x-6 ?

The integral of f(x)=5x-6 is (5x^2)/2-6x+C

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Find the Antiderivative f(x)=5x-6

integral

f (x) = 5 x - 6

\frac{5 x ^{2}}{2} - 6 x + C

Solution steps

\int 5 x - 6 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 5 x d x - \int 6 d x

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

\int 6 d x = 6 x

= \frac{5 x ^{2}}{2} - 6 x

Add a constant to the solution

= \frac{5 x ^{2}}{2} - 6 x + C

x \to 0 lim (\frac{( e ^{5 x} - 1 - 5 x )}{( x ^{2} )})

- \frac{d}{d x} y = \frac{4}{x}

- \frac{d}{d x} (\frac{1}{x})

- \frac{d}{d x} y = 3 x

(2, 5), (3, 6)