What is the integral of 5(3x-1)7 ?

The integral of 5(3x-1)7 is 35((3x^2)/2-x)+C

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integral of 5(3x-1)7

\int 5 (3 x - 1) 7 d x

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

Solution steps

\int 5 (3 x - 1) \cdot 7 d x

Take the constant out:

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

= 5 \cdot 7 \cdot \int 3 x - 1 d x

Simplify

= 35 \cdot \int 3 x - 1 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

= 35 (\int 3 x d x - \int 1 d x)

\int 3 x d x = \frac{3 x ^{2}}{2}

\int 1 d x = x

= 35 (\frac{3 x ^{2}}{2} - x)

Add a constant to the solution

= 35 (\frac{3 x ^{2}}{2} - x) + C

ln (3 - x)

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