1）∫√(2+3x)dx
t=2+3x,x=1/3*t-2/3,dx=1/3dt
）∫√(2+3x)dx=St^(1/2)*1/3dt=1/3*2/3*t^(3/2)+c=2/9*(2+3x)^(3/2)+c
2）∫4/(1-2x)^2dx
t=1-2x,x=-1/2*t+1/2,dx=-dt
）∫4/(1-2x)^2dx=S4/t^2 *(-dt)=-4St^(-2)*dt=4/t+c=4/(1-2x)+c
3）∫sin3xdx
t=3x,x=1/3*t,dx=1/3*dt
∫sin3xdx=Ssint*1/3*dt=1/3*Ssintdt=-1/3*cost+c=-1/3*cos3x+c
4）∫dx/√(1-25x^2)
x=1/5*sint,t=arcsin(5x),dx=1/5*costdt
∫dx/√(1-25x^2)=S1/5*costdt/cost=1/5*Sdt=t/5+c=1/5*arcsin(x/5)+c
5）∫dx/1+9x^2
x=1/3*tant,t=arctan(3x),dx=1/3*(sect)^2dt
∫dx/1+9x^2=S1/3*(sect)^2dt/sect=1/3*Ssectdt=1/3*ln|tan(t/2+pi/4)|+c
t=arctan(3x),代入化简即可
6）∫cos^3xdx=S（1-(sinx)^2)*cosxdx=S(1-(sinx)^2)dsinx=sinx-1/3*(sinx)^3+c