What is the integral of 34x+20*(-1/10)x+1 ?

The integral of 34x+20*(-1/10)x+1 is 16x^2+x+C

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integral of 34x+20*(-1/10)x+1

\int 34 x + 20 \cdot (- \frac{1}{10}) x + 1 d x

16 x^{2} + x + C

Solution steps

\int 34 x + 20 (- \frac{1}{10}) x + 1 d x

Simplify

34 x + 20 (- \frac{1}{10}) x + 1 : 32 x + 1

= \int 32 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

= \int 32 x d x + \int 1 d x

\int 32 x d x = 16 x^{2}

\int 1 d x = x

= 16 x^{2} + x

Add a constant to the solution

= 16 x^{2} + x + C

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What is the integral of 34x+20*(-1/10)x+1 ?
The integral of 34x+20*(-1/10)x+1 is 16x^2+x+C