1 / | | 1 | 1*------- dx | 4 | cos (x) | / 0
Integral(1/cos(x)^4, (x, 0, 1))
Rewrite the integrand:
There are multiple ways to do this integral.
Let .
Then let and substitute :
Integrate term-by-term:
The integral of is when :
The integral of a constant is the constant times the variable of integration:
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 result is:
Rewrite the integrand:
Integrate term-by-term:
Let .
Then let and substitute :
The integral of is when :
Now substitute back in:
The result is:
Add the constant of integration:
The answer is:
/ | 3 | 1 tan (x) | 1*------- dx = C + ------- + tan(x) | 4 3 | cos (x) | /
sin(1) 2*sin(1) --------- + -------- 3 3*cos(1) 3*cos (1)
=
sin(1) 2*sin(1) --------- + -------- 3 3*cos(1) 3*cos (1)
Use the examples entering the upper and lower limits of integration.