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