Question

помогите, пожалуйста

Answer 1

10.28.

$\int {\frac{dx}{e^{2x-1}}} = \int {e^{-(2x-1)} \, dx} =-\frac{1}{2} \int {e^{-2x+1} \, d(-2x+1)} = -\frac{1}{2}\cdot e^{-2x+1} +C= \\ \\ = -\frac{1}{2}\cdot e^{1-2x} +C$

10.30.

$\int {\frac{dx}{(4x+3)^5}}=\int {(4x+3)^{-5} \, dx}=\frac{1}{4}\int{(4x+3)^{-5} \, d(4x+3)}= \\ \\ =\frac{1}{4}\cdot (-\frac{1}{4})\cdot (4x+3)^{-4}+C= -\frac{1}{16}\cdot\frac{1}{(4x+3)^4}+C$

10.32.

$\int {\frac{dx}{\sqrt{2-x}}}=\int {(2-x)^{-\frac{1}{2}}} \, dx = - \int {(2-x)^{-\frac{1}{2}} \, d(2-x)}=-\frac{1}{\frac{1}{2}}}\cdot (2-x)^\frac{1}{2}+C=\\ \\ =-2\sqrt{2-x}+C$