Can we use substitution variable in only one of the two

[lucky_luke]

hi

#If {int}(A + B)dx has two terms A and B, can we use substitution variable in only one of the two terms? Can you provide me with an example?

#Can you show me how we would find antiderivative of {int} sin[2x] using

sin(x)*cos(x) = 1/2*( sin(x1+x2) + cos(x1-x1) )

with the help of substitution variable?


thank you

 

[daon]

Yes, but you would have to separate the integral.

\(\displaystyle \int(A+B)dx = \int Adx + \int Bdx\)

The equation A may require substitution to solve, but B may be a straight-forward integral.

For your Sin(2x) question, I do not see the connection you are attempting to make. SIn2x is a straight-forward integral with U=2x.