3 / | | tan(4*x - 2) dx | / 1
Integral(tan(4*x - 2), (x, 1, 3))
Rewrite the integrand:
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:
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
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:
So, the result is:
Now substitute back in:
Now simplify:
Add the constant of integration:
The answer is:
/ | log(cos(4*x - 2)) | tan(4*x - 2) dx = C - ----------------- | 4 /
/ 2 \ / 2 \ log\1 + tan (2)/ log\1 + tan (10)/ - ---------------- + ----------------- 8 8
=
/ 2 \ / 2 \ log\1 + tan (2)/ log\1 + tan (10)/ - ---------------- + ----------------- 8 8
-log(1 + tan(2)^2)/8 + log(1 + tan(10)^2)/8
Use the examples entering the upper and lower limits of integration.