Х=12/17 - 5/17
х=7/17
х=7/17-2/17
х=5/17
Здесь надо воспользоваться универсальной тригонометрической подстановкой:
![\int\limits {\frac{1+sinx}{1+cosx+sinx}} \, dx =\begin{vmatrix}tg\frac{x}{2}=t; \ \ sinx=\frac{2t}{1+t^2}\\ \\ cosx=\frac{1-t^2}{1+t^2}; \ dx=\frac{2dt} {1+t^2}\end{vmatrix}=\int\limits {\frac{1+\frac{2t}{1+t^2}}{1+\frac{1-t^2}{1+t^2}+\frac{2t}{1+t^2}}} *\frac{2dt} {1+t^2} = \\\\ \\ =2\int\limits {\frac{1+\frac{2t} {1+t^2}}{1+t^2+1-t^2+2t}} \, dt= 2\int\limits {\frac{\frac{1+t^2+2t} {1+t^2}}{2+2t}} \, dt= 2\int\limits {\frac{t^2+2t+1}{2(t+1)(t^2+1)}} \, dx =](https://tex.z-dn.net/?f=+%5Cint%5Climits+%7B%5Cfrac%7B1%2Bsinx%7D%7B1%2Bcosx%2Bsinx%7D%7D+%5C%2C+dx++%3D%5Cbegin%7Bvmatrix%7Dtg%5Cfrac%7Bx%7D%7B2%7D%3Dt%3B+%5C+%5C+sinx%3D%5Cfrac%7B2t%7D%7B1%2Bt%5E2%7D%5C%5C+%5C%5C+cosx%3D%5Cfrac%7B1-t%5E2%7D%7B1%2Bt%5E2%7D%3B+%5C+dx%3D%5Cfrac%7B2dt%7D+%7B1%2Bt%5E2%7D%5Cend%7Bvmatrix%7D%3D%5Cint%5Climits+%7B%5Cfrac%7B1%2B%5Cfrac%7B2t%7D%7B1%2Bt%5E2%7D%7D%7B1%2B%5Cfrac%7B1-t%5E2%7D%7B1%2Bt%5E2%7D%2B%5Cfrac%7B2t%7D%7B1%2Bt%5E2%7D%7D%7D++%2A%5Cfrac%7B2dt%7D+%7B1%2Bt%5E2%7D+%3D+%5C%5C%5C%5C+%5C%5C+%3D2%5Cint%5Climits+%7B%5Cfrac%7B1%2B%5Cfrac%7B2t%7D+%7B1%2Bt%5E2%7D%7D%7B1%2Bt%5E2%2B1-t%5E2%2B2t%7D%7D+%5C%2C+dt%3D++2%5Cint%5Climits+%7B%5Cfrac%7B%5Cfrac%7B1%2Bt%5E2%2B2t%7D+%7B1%2Bt%5E2%7D%7D%7B2%2B2t%7D%7D+%5C%2C+dt%3D++2%5Cint%5Climits+%7B%5Cfrac%7Bt%5E2%2B2t%2B1%7D%7B2%28t%2B1%29%28t%5E2%2B1%29%7D%7D+%5C%2C+dx++%3D+)
![\int\limits {\frac{(t+1)^2}{(t+1)(t^2+1)}} dt = \int\limits {\frac{t+1}{t^2+1}} dt =\int\limits {\frac{t}{t^2+1}} dt +\int\limits {\frac{1}{t^2+1}} dt =\frac{1}{2}\int\limits {\frac{1}{t^2+1}} d(t^2+1) + \\ \\ +arctgt+C=\frac{1}{2} \ln |t^2+1|+arctgt+C =\begin{vmatrix}t=tg\frac{x}{2} \end{vmatrix}=\\ \\ = \frac{1}{2} \ln |tg^2(\frac{x}{2})+1|+\frac{x}{2} +C](https://tex.z-dn.net/?f=++%5Cint%5Climits+%7B%5Cfrac%7B%28t%2B1%29%5E2%7D%7B%28t%2B1%29%28t%5E2%2B1%29%7D%7D++dt++%3D+%5Cint%5Climits+%7B%5Cfrac%7Bt%2B1%7D%7Bt%5E2%2B1%7D%7D++dt++%3D%5Cint%5Climits+%7B%5Cfrac%7Bt%7D%7Bt%5E2%2B1%7D%7D++dt++%2B%5Cint%5Climits+%7B%5Cfrac%7B1%7D%7Bt%5E2%2B1%7D%7D++dt++%3D%5Cfrac%7B1%7D%7B2%7D%5Cint%5Climits+%7B%5Cfrac%7B1%7D%7Bt%5E2%2B1%7D%7D++d%28t%5E2%2B1%29+++%2B+%5C%5C+%5C%5C+%2Barctgt%2BC%3D%5Cfrac%7B1%7D%7B2%7D+%5Cln+%7Ct%5E2%2B1%7C%2Barctgt%2BC+%3D%5Cbegin%7Bvmatrix%7Dt%3Dtg%5Cfrac%7Bx%7D%7B2%7D+%5Cend%7Bvmatrix%7D%3D%5C%5C+%5C%5C+%3D+%5Cfrac%7B1%7D%7B2%7D+%5Cln+%7Ctg%5E2%28%5Cfrac%7Bx%7D%7B2%7D%29%2B1%7C%2B%5Cfrac%7Bx%7D%7B2%7D+%2BC+)
Можно так ответ и оставить, а можно еще немного упростить:
![\frac{1}{2} \ln |tg^2(\frac{x}{2})+1|+\frac{x}{2} +C = \frac{1}{2} \ln |\frac{1}{cos^2(\frac{x}{2})}|+\frac{x}{2} +C =\\ \\ =\frac{1}{2} \ln |cos^{-2}(\frac{x}{2})|+\frac{x}{2} +C =\frac{x}{2} - \ln|cos\frac{x}{2} |+C\\ \\ OTBET: \ \frac{x}{2} - \ln|cos\frac{x}{2} |+C](https://tex.z-dn.net/?f=++%5Cfrac%7B1%7D%7B2%7D+%5Cln+%7Ctg%5E2%28%5Cfrac%7Bx%7D%7B2%7D%29%2B1%7C%2B%5Cfrac%7Bx%7D%7B2%7D+%2BC+%3D+%5Cfrac%7B1%7D%7B2%7D+%5Cln+%7C%5Cfrac%7B1%7D%7Bcos%5E2%28%5Cfrac%7Bx%7D%7B2%7D%29%7D%7C%2B%5Cfrac%7Bx%7D%7B2%7D+%2BC+++%3D%5C%5C+%5C%5C+%3D%5Cfrac%7B1%7D%7B2%7D+%5Cln+%7Ccos%5E%7B-2%7D%28%5Cfrac%7Bx%7D%7B2%7D%29%7C%2B%5Cfrac%7Bx%7D%7B2%7D+%2BC+++%3D%5Cfrac%7Bx%7D%7B2%7D+-+%5Cln%7Ccos%5Cfrac%7Bx%7D%7B2%7D+%7C%2BC%5C%5C+%5C%5C+OTBET%3A+%5C+%5Cfrac%7Bx%7D%7B2%7D+-+%5Cln%7Ccos%5Cfrac%7Bx%7D%7B2%7D+%7C%2BC+)
Cos(3x-π/4)=√2/2
3x-π/4=π/4+2πk U 3x-π/4=-π/4+2πk
3x=π/2+2πk U 3x=2πk
x=π/6+2πk/3 U x=2πk/3,k∈z
<span>7•10³+5•10²+8•(-10)²=7000+500+800=8300
</span>
А=46см. S=а*b S=46*18=828(см.)
b=18см. 828:4=207(см.)
Разбили на 4 части
S-?см.(квадратных)