What is the integral of (80-3t-(2t+30)) ?

The integral of (80-3t-(2t+30)) is -(5t^2)/2+50t+C

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integral of (80-3t-(2t+30))

\int (80 - 3 t - (2 t + 30)) d t

- \frac{5 t ^{2}}{2} + 50 t + C

Solution steps

\int 80 - 3 t - (2 t + 30) d t

Simplify

= \int - 5 t + 50 d t

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 t d t + \int 50 d t

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

\int 50 d t = 50 t

= - \frac{5 t ^{2}}{2} + 50 t

Add a constant to the solution

= - \frac{5 t ^{2}}{2} + 50 t + C

\frac{d}{d x} (\frac{x - x ^{2}}{2 - 3 x + x ^{2}})

\int_{0}^{l n (6)} e^{x} - e^{- 3 x} d x

y = \frac{4 x}{9 - tan ( x )}

arctan (x)

\int_{0}^{1} (x 2 - x^{2}) d x

What is the integral of (80-3t-(2t+30)) ?
The integral of (80-3t-(2t+30)) is -(5t^2)/2+50t+C