Question

$\tt \displaystyle \int \: \frac{x}{2} +5dx$
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Answer 1

$\tt \displaystyle \int \: \tt \frac{x}{2} +5dx \\ \\\tt \displaystyle \int \tt \frac{x}{2} dx + \tt \displaystyle \tt \int5dx \\ \\\tt \frac{1}{2} \displaystyle \int \: \tt xdx + \tt \displaystyle \tt \int5dx \\ \\\tt \frac{1}{2} ( \frac{1}{2} x ^{2} + C) + \tt \displaystyle \tt \int5dx \\ \\\tt \frac{1}{2} ( \frac{1}{2} x ^{2} + C) + 5x + c \\ \\\tt \red{ \frac{1}{4} x ^{2}+ 5x + C }$

Answer 2

$\Large\boxed{\begin{array}{l}\displaystyle\sf\int\bigg(\dfrac{x}{2}+5\bigg)dx=\dfrac{1}{2}\int x~dx+5\int dx\\\sf=\dfrac{1}{2}\cdot\dfrac{1}{2}x^2+5x+C\\\displaystyle\sf\int\bigg(\dfrac{x}{2}+5\bigg)dx=\dfrac{1}{4}x^2+5x+C\end{array}}$