Use the trigonometric relation now use the binomial expansion. Apply this to the above integrals.
Second integral becomes
Now use the recursion relationship on each integral.
Apply the same principle to the first integral as well.
I'm supposed to convert the even powers of tangent to secant using a recursion formula, repeatedly if necessary, and then evaluate.
Here are to two problems:
∫ tan^2(x)sec(x) dx
∫ tan^4(x)sec(x) dx
Here is the recursion formula:
∫ sec^n(x) dx = (tan(x)sec^(n-2)(x))/(n-1) - ((n-2)/(n-1))⋅∫ sec^(n-2)(x) dx
I'm not sure how to go about this, so can someone please help me? Thanks!
Use the trigonometric relation now use the binomial expansion. Apply this to the above integrals.
Second integral becomes
Now use the recursion relationship on each integral.
Apply the same principle to the first integral as well.
Hello, Preston019!
There is a typo in the Recursion Formua.
There should be a plus (+) between the two expressions.
I'm supposed to convert the even powers of tangent to secant using a recursion formula,
repeatedly if necessary, and then evaluate.
. . . . . . . . . .
. . . . . . . . . . .
Integral [2] has a standard formula: .
We will apply the Recursion Formula to integral [1].
Substitute
. . . . . . . . .
. . . . . .