1 / | | 3/x\ | tan |-| dx | \3/ | / 0
Integral(tan(x/3)^3, (x, 0, 1))
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:
Let .
Then let and substitute :
Rewrite the integrand:
Integrate term-by-term:
The integral of a constant is the constant times the variable of integration:
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:
The result is:
Now substitute back in:
So, the result is:
Now substitute back in:
Rewrite the integrand:
Integrate term-by-term:
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 a constant is the constant times the variable of integration:
So, the result is:
Now substitute back in:
The integral of a constant times a function is the constant times the integral of the function:
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:
So, the result is:
The result is:
Rewrite the integrand:
Integrate term-by-term:
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 a constant is the constant times the variable of integration:
So, the result is:
Now substitute back in:
The integral of a constant times a function is the constant times the integral of the function:
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:
So, the result is:
The result is:
Add the constant of integration:
The answer is:
/ / 2/x\\ 2/x\ | 3*log|3*sec |-|| 3*sec |-| | 3/x\ \ \3// \3/ | tan |-| dx = C - ---------------- + --------- | \3/ 2 2 | /
3 3 - - + 3*log(cos(1/3)) + ----------- 2 2 2*cos (1/3)
=
3 3 - - + 3*log(cos(1/3)) + ----------- 2 2 2*cos (1/3)
Use the examples entering the upper and lower limits of integration.