What is the integral from 2 to x of 5t+3 ?

The integral from 2 to x of 5t+3 is 3x+5*(x^2)/2-16

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integral from 2 to x of 5t+3

\int_{2}^{x} 5 t + 3 d t

3 x + 5 \cdot \frac{x ^{2}}{2} - 16

Solution steps

\int_{2}^{x} 5 t + 3 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_{2}^{x} 5 t d t + \int_{2}^{x} 3 d t

\int_{2}^{x} 5 t d t = 5 (\frac{x ^{2}}{2} - 2)

\int_{2}^{x} 3 d t = 3 x - 6

= 5 (\frac{x ^{2}}{2} - 2) + 3 x - 6

Simplify

5 (\frac{x ^{2}}{2} - 2) + 3 x - 6 : 3 x + 5 \cdot \frac{x ^{2}}{2} - 16

= 3 x + 5 \cdot \frac{x ^{2}}{2} - 16

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What is the integral from 2 to x of 5t+3 ?
The integral from 2 to x of 5t+3 is 3x+5*(x^2)/2-16