# Combine the integrals into one integral, then evaluate the integral. ∫(7x+4)dx+∫(7x+5)dx

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## Answered question

2021-11-08

Combine the integrals into one integral, then evaluate the integral.

$\int (7x+4)dx+\int (7x+5)dx$

### Answer & Explanation

Step 1

To evaluate,

$\int (7x+4)dx+\int (7x+5)dx$

Step 2

We know that,

$\int f\left(x\right)dx+\int g\left(x\right)dx=\int (f\left(x\right)+g\left(x\right))dx$

Now,

$\int (7x+4)dx+\int (7x+5)dx$

$=\int ((7x+4)+(7x+5))dx$

$=\int (7x+4+7x+5)dx$

$=\int (14x+9)dx$

$=14\times \frac{{x}^{2}}{2}+9x+c$

$=7{x}^{2}+9x+c$

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