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2021-11-08

Combine the integrals into one integral, then evaluate the integral.
$\int \left(7x+4\right)dx+\int \left(7x+5\right)dx$

Tuthornt

Step 1
To evaluate,
$\int \left(7x+4\right)dx+\int \left(7x+5\right)dx$
Step 2
We know that,
$\int f\left(x\right)dx+\int g\left(x\right)dx=\int \left(f\left(x\right)+g\left(x\right)\right)dx$
Now,
$\int \left(7x+4\right)dx+\int \left(7x+5\right)dx$
$=\int \left(\left(7x+4\right)+\left(7x+5\right)\right)dx$
$=\int \left(7x+4+7x+5\right)dx$
$=\int \left(14x+9\right)dx$
$=14×\frac{{x}^{2}}{2}+9x+c$
$=7{x}^{2}+9x+c$

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