What is the integral of-14/15*(x-30)+14 ?

The integral of-14/15*(x-30)+14 is -(7x^2)/(15)+42x+C

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integral of-14/15*(x-30)+14

\int - \frac{14}{15} \cdot (x - 30) + 14 d x

- \frac{7 x ^{2}}{15} + 42 x + C

Solution steps

\int - \frac{14}{15} (x - 30) + 14 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 \frac{14}{15} (x - 30) d x + \int 14 d x

\int \frac{14}{15} (x - 30) d x = \frac{14}{15} (\frac{x ^{2}}{2} - 30 x)

\int 14 d x = 14 x

= - \frac{14}{15} (\frac{x ^{2}}{2} - 30 x) + 14 x

Simplify

- \frac{14}{15} (\frac{x ^{2}}{2} - 30 x) + 14 x : - \frac{7 x ^{2}}{15} + 42 x

= - \frac{7 x ^{2}}{15} + 42 x

Add a constant to the solution

= - \frac{7 x ^{2}}{15} + 42 x + C

\frac{d y}{d x} = e^{2 x - 1} y^{2}

\int \frac{x ^{2} + 25}{x ^{2}} d x

x = y^{2}, x = 2 - y

f (x) = \frac{- 4 x}{x ^{2} + 1}, (- 1, 2)

cos (θ^{2})

What is the integral of-14/15*(x-30)+14 ?
The integral of-14/15*(x-30)+14 is -(7x^2)/(15)+42x+C