What is the integral of 20(50+x) ?

The integral of 20(50+x) is 20(50x+(x^2)/2)+C

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integral of 20(50+x)

\int 20 (50 + x) d x

20 (50 x + \frac{x ^{2}}{2}) + C

Solution steps

\int 20 (50 + x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 20 \cdot \int 50 + x 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

= 20 (\int 50 d x + \int x d x)

\int 50 d x = 50 x

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

= 20 (50 x + \frac{x ^{2}}{2})

Add a constant to the solution

= 20 (50 x + \frac{x ^{2}}{2}) + C

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What is the integral of 20(50+x) ?
The integral of 20(50+x) is 20(50x+(x^2)/2)+C