1
t=9+x²,dt=2xdx
![\int\limits {3x/ \sqrt{9+x^2} } \, dx =3/2 \int\limits {1/ \sqrt{t} } \, dt =3 \sqrt{t} =3 \sqrt{9+x^2} +C](https://tex.z-dn.net/?f=+%5Cint%5Climits+%7B3x%2F+%5Csqrt%7B9%2Bx%5E2%7D+%7D+%5C%2C+dx+%3D3%2F2+%5Cint%5Climits+%7B1%2F+%5Csqrt%7Bt%7D+%7D+%5C%2C+dt+%3D3+%5Csqrt%7Bt%7D+%3D3+%5Csqrt%7B9%2Bx%5E2%7D+%2BC)
2
t=2x+1,dt=2dx
u=t,du=dt
df=dt,f=e^t
![\int\limits {e^(2x+1)*3x} \, dx =3/2 \int\limits {1/2*e^t*(t-1)} \, dt=3/4*e^t*t-3/2](https://tex.z-dn.net/?f=+%5Cint%5Climits+%7Be%5E%282x%2B1%29%2A3x%7D+%5C%2C+dx+%3D3%2F2+%5Cint%5Climits+%7B1%2F2%2Ae%5Et%2A%28t-1%29%7D+%5C%2C+dt%3D3%2F4%2Ae%5Et%2At-3%2F2+++)
![\int\limits {e^t} \, dt =3/4*e^t*t-3/2*e^t=3/4*e^(2x+1) *(2x+1)-3/2*e^(2x](https://tex.z-dn.net/?f=+%5Cint%5Climits+%7Be%5Et%7D+%5C%2C+dt+%3D3%2F4%2Ae%5Et%2At-3%2F2%2Ae%5Et%3D3%2F4%2Ae%5E%282x%2B1%29+%2A%282x%2B1%29-3%2F2%2Ae%5E%282x)
![+1)=3/4*e^(2x+1)*(2x-1)+C](https://tex.z-dn.net/?f=%2B1%29%3D3%2F4%2Ae%5E%282x%2B1%29%2A%282x-1%29%2BC)
3
Найдем пределы интегрирования
x²+x+1=-2x-1
x²+3x+2=0
x1=x2=-3 U x1*x2=2
x1=-2 U x2=-1
![S= \int\limits {(-x^2-3x-2)} \, dx =-x^3/3-3x^2/2-2x|-1-(-2)=1/3-](https://tex.z-dn.net/?f=S%3D+%5Cint%5Climits+%7B%28-x%5E2-3x-2%29%7D+%5C%2C+dx+%3D-x%5E3%2F3-3x%5E2%2F2-2x%7C-1-%28-2%29%3D1%2F3-)
![3/2+2-8/3+6-4=1/6](https://tex.z-dn.net/?f=3%2F2%2B2-8%2F3%2B6-4%3D1%2F6)
4
![\int\limits^4_0 {(4x+x^3)} \, dx =2x^2+x^4/4|4-0=8+4=12](https://tex.z-dn.net/?f=+%5Cint%5Climits%5E4_0+%7B%284x%2Bx%5E3%29%7D+%5C%2C+dx+%3D2x%5E2%2Bx%5E4%2F4%7C4-0%3D8%2B4%3D12)
1)x/2+3x+5/2-3x=15x+10/4-9x^2
x(2-3x)+5(2+3x)=15x+10
2x-3x^2+10+15x-15x-10=0
2x-3x^2=0
x(2-3x)=0
x=0
x=2/3
2)(x+5)(3-x) +(7-3x) (3-x) =5(7-3x)
3x-x^2+15-5x+21-7x-9x+4x^2=35-15x
дальше саи
17*19+17*45-17*14=323+765-238=850
12*32-12*18+38*14=384-216+532=700