Question

Evaluate the following integration w.r.t. $x$
$\int [(9-\frac{x}{8})+(4x+5{)}^3]dx$

Answer 1

$\int [(9-\frac{x}{8})+(4x+5{)}^3]dx$

$=\int [(9-\frac{x}{8})+64x^3+1)5+80x^2+100x]dx$

$=\int [134+\frac{799}{8}x+80x^2+64x^3]dx$

$=134x+\frac{799}{16}{x}^2+\frac{80}{3}{x}^3+\frac{64}{4}{x}^4+C$

$=134x+\frac{799}{16}{x}^2+\frac{80}{3}{x}^3+16x^4+C$

$\therefore \int [(9-\frac{x}{8})+(4x+5{)}^3]dx=134x+\frac{799}{16}{x}^2+\frac{80}{3}{x}^3+16x^4+C$.