X(4-9x)=0
x1=0 4-9x=0
-9x=-4
x=4\9
16/х = 4/5
4х=16*5
4х=80
х=80/4
х=20
⇒ 16/20 = 4/5
22/35 = 242/х
22х=242*35
22х=8470
х=8470/22
х=385
⇒ 22/35 = 242/385
0,45/у = 5/2,7
5у=0,45*2,7
5у=1,215
у=1,215/5
у=0,243
⇒ 0,45/0,243 = 5/2,7
2,5/0,38 = 6,5/у
2,5у=0,38*6,5
2,5у=2,47
у=2,47/2,5
у=0,988
⇒ 2,5/0,38 = 6,5/0,988
х/5,5 = 70/0,11
0,11х=5,5*70
0,11х=385
х=385/0,11
х=3500
⇒ 3500/5,5 = 70/0,11
17/81 = у/72
81у=17*72
81у=1224
у=1224/81
у=15 9/81
у=15 1/9
⇒ 17/81 = 15 1/9 / 72
в таких заданиях записывайте пропорцию
а затем крест-накрест перемножайте, а далее решайте как обычное уравнение.
![1)\; \; \int \frac{lny\cdot dy}{y^2}=[\, u=lny\; ,\; du=\frac{dy}{y}\; ,\; dv=\frac{dy}{y^2}\; ,\; v=\int \frac{dy}{y^2}=\int y^{-2}dy=\\\\= \frac{y^{-1}}{-1}=-\frac{1}{y}\, ]=[\, \int u\, dv=uv-\int v\, du]=\\\\=- \frac{lny}{y}+\int \frac{dy}{y^2}=-\frac{lny}{y}-\frac{1}{y} +C\\\\3)\; \; \int \frac{dz}{1-sinz}=[\, t=tg\frac{z}{2},\; sinz=\frac{2t}{1+t^2}\; ,\; dz=\frac{2\, dt}{1+t^2}\, ]=\\\\=\int \frac{2\, dt}{(1+t^2)\cdot (1-\frac{2t}{1+t^2})}=2\int \frac{dt}{t^2-2t+1}=2\int \frac{dt}{(t-1)^2} =2\cdot \frac{(t-1)^{-1}}{-1}=](https://tex.z-dn.net/?f=1%29%5C%3B+%5C%3B+%5Cint+%5Cfrac%7Blny%5Ccdot+dy%7D%7By%5E2%7D%3D%5B%5C%2C+u%3Dlny%5C%3B+%2C%5C%3B+du%3D%5Cfrac%7Bdy%7D%7By%7D%5C%3B+%2C%5C%3B+dv%3D%5Cfrac%7Bdy%7D%7By%5E2%7D%5C%3B+%2C%5C%3B+v%3D%5Cint+%5Cfrac%7Bdy%7D%7By%5E2%7D%3D%5Cint+y%5E%7B-2%7Ddy%3D%5C%5C%5C%5C%3D+%5Cfrac%7By%5E%7B-1%7D%7D%7B-1%7D%3D-%5Cfrac%7B1%7D%7By%7D%5C%2C+%5D%3D%5B%5C%2C+%5Cint+u%5C%2C+dv%3Duv-%5Cint+v%5C%2C+du%5D%3D%5C%5C%5C%5C%3D-+%5Cfrac%7Blny%7D%7By%7D%2B%5Cint+%5Cfrac%7Bdy%7D%7By%5E2%7D%3D-%5Cfrac%7Blny%7D%7By%7D-%5Cfrac%7B1%7D%7By%7D+%2BC%5C%5C%5C%5C3%29%5C%3B+%5C%3B+%5Cint+%5Cfrac%7Bdz%7D%7B1-sinz%7D%3D%5B%5C%2C+t%3Dtg%5Cfrac%7Bz%7D%7B2%7D%2C%5C%3B+sinz%3D%5Cfrac%7B2t%7D%7B1%2Bt%5E2%7D%5C%3B+%2C%5C%3B+dz%3D%5Cfrac%7B2%5C%2C+dt%7D%7B1%2Bt%5E2%7D%5C%2C+%5D%3D%5C%5C%5C%5C%3D%5Cint+%5Cfrac%7B2%5C%2C+dt%7D%7B%281%2Bt%5E2%29%5Ccdot+%281-%5Cfrac%7B2t%7D%7B1%2Bt%5E2%7D%29%7D%3D2%5Cint+%5Cfrac%7Bdt%7D%7Bt%5E2-2t%2B1%7D%3D2%5Cint+%5Cfrac%7Bdt%7D%7B%28t-1%29%5E2%7D+%3D2%5Ccdot+%5Cfrac%7B%28t-1%29%5E%7B-1%7D%7D%7B-1%7D%3D)
![=- \frac{2}{t-1}+C=- \frac{2}{tg\frac{x}{2}-1}+C\\\\\\\star \; \; \int (ax+b)^{n}= \frac{1}{a}\cdot \frac{(ax+b)^{n+1}}{n+1} +C\; \; ,\; \; ax+b=t-1\; ,\; a=1\; ,\; n=-2](https://tex.z-dn.net/?f=%3D-+%5Cfrac%7B2%7D%7Bt-1%7D%2BC%3D-+%5Cfrac%7B2%7D%7Btg%5Cfrac%7Bx%7D%7B2%7D-1%7D%2BC%5C%5C%5C%5C%5C%5C%5Cstar+%5C%3B+%5C%3B+%5Cint+%28ax%2Bb%29%5E%7Bn%7D%3D+%5Cfrac%7B1%7D%7Ba%7D%5Ccdot+%5Cfrac%7B%28ax%2Bb%29%5E%7Bn%2B1%7D%7D%7Bn%2B1%7D+%2BC%5C%3B+%5C%3B+%2C%5C%3B+%5C%3B+ax%2Bb%3Dt-1%5C%3B+%2C%5C%3B+a%3D1%5C%3B+%2C%5C%3B+n%3D-2)
P.S. Во 2 примере ошибка в условии.