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