Question

Evaluate:$\int ({3\sec }^{2}x-\frac{4}{x}+\frac{1}{x\sqrt{x}}-7)dx$

Answer 1

$\int (3se{c}^{2}x-\frac{4}{x}+\frac{1}{x\sqrt{x}}-7)dx=3\int se{c}^{2}xdx-4\int \frac{dx}{x}+\int x^{-3/2}dx-\int 7dx$

$=3tanx-4logx+\frac{x^{-3/2+1}}{\frac{-3}{2}+1}-7x+c$

$=3tanx-4logx-\frac{2}{\sqrt{x}}-7x+c$