1 / | | 1 | 1*------------------ dz | 5*z + tan(y - 3*x) | / 0
Integral(1/(5*z + tan(y - 3*x)), (z, 0, 1))
There are multiple ways to do this integral.
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
The integral of is .
So, the result is:
Now substitute back in:
Rewrite the integrand:
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
The integral of is .
So, the result is:
Now substitute back in:
Rewrite the integrand:
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
The integral of is .
So, the result is:
Now substitute back in:
Now simplify:
Add the constant of integration:
The answer is:
/ | | 1 log(5*z + tan(y - 3*x)) | 1*------------------ dz = C + ----------------------- | 5*z + tan(y - 3*x) 5 | /
log(-tan(-y + 3*x)) log(5 - tan(-y + 3*x)) - ------------------- + ---------------------- 5 5
=
log(-tan(-y + 3*x)) log(5 - tan(-y + 3*x)) - ------------------- + ---------------------- 5 5
Use the examples entering the upper and lower limits of integration.