What is the integral of (2.286x-2.5(x-3)-3(x-5)) ?

The integral of (2.286x-2.5(x-3)-3(x-5)) is -1.607x^2+22.5x+C

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integral of (2.286x-2.5(x-3)-3(x-5))

\int (2.286 x - 2.5 (x - 3) - 3 (x - 5)) d x

- 1.607 x^{2} + 22.5 x + C

Solution steps

\int 2.286 x - 2.5 (x - 3) - 3 (x - 5) d x

Simplify

2.286 x - 2.5 (x - 3) - 3 (x - 5) : - 3.214 x + 22.5

= \int - 3.214 x + 22.5 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 3.214 x d x + \int 22.5 d x

\int 3.214 x d x = 1.607 x^{2}

\int 22.5 d x = 22.5 x

= - 1.607 x^{2} + 22.5 x

Add a constant to the solution

= - 1.607 x^{2} + 22.5 x + C

- 6 e^{- x^{2}} x

\int \frac{1}{x} d x

y = x^{2} + 4, y = 7 - 2 x^{2}

\int_{\frac{1}{2}}^{1} \frac{2 y + 3}{y ^{2} + y} d y

y^{^{''}} + 9 y = cos (3 t)

What is the integral of (2.286x-2.5(x-3)-3(x-5)) ?
The integral of (2.286x-2.5(x-3)-3(x-5)) is -1.607x^2+22.5x+C