Posted by **Sean** on Thursday, March 13, 2008 at 2:43pm.

What is the indefinite integral of:

(12sin(3x)cscx)dx

If I could have two things given to me please, I'd be grateful. The two things are:

1) Trick/Technique to Use

2) First 2 or 3 steps

Thanks in advanced.

- Calculus III -
**Count Iblis**, Thursday, March 13, 2008 at 5:58pm
Express sin(3x) in terms of sin(x).

exp(ix) = cos(x) + i sin(x) (1)

Take the third power of both sides:

exp(3ix) = [cos(x) + i sin(x)]^3

From (1) it follows that the imaginary part of the left hand side is sin(3x)

Expand the right hand side and take the imaginary part. You then find:

sin(3x) = -sin^3(x) + 3sin(x)cos^2(x)

= 3 sin(x) - 4 sin^3(x)

It then follws that:

sin(3x)/sin(x) =

3 - 4 sin^2(x)

which is almost trivial to integrate.

- Calculus III -
**Sean**, Thursday, March 13, 2008 at 7:01pm
Out of curiosity, where did the 'i' come from, and what technique did you use?

Also, how did you write sin(3x) In terms of sin(x)?

## Answer this Question

## Related Questions

- Calculus II - 1) Compute the indefinite integral: integral 2x ln(x^2 - 8x + 18) ...
- Calculus - I have two questions, because I'm preparing for a math test on monday...
- Math - 1. Evaluate the indefinite integral ([6x^2 + 12x^(3/2) +4x+9]/sqrt x)dx. ...
- Calc BC - 1. Find the indefinite integral. Indefinite integral tan^3(pix/7)sec^2...
- Calculus - Solve these indefinite and definite integrals. [integration sign] 4j-...
- Calculus II/III - A. Find the integral of the following function. Integral of (x...
- Calculus - Would someone please tell me how to solve these two problems? Find ...
- Calculus - Hello Everyone, I need help with Calc II. 1. Integral from 0 to 1 of...
- Calculus Please Help - Evaluate the indefinite integral Note: Use an upper-case...
- calc - how do you start this problem: integral of xe^(-2x) There are two ways: 1...