How do you integrate #y=sinx/tanx# using the quotient rule?

1 Answer
Steve M
Nov 13, 2016

# int sinx/tanx dx = sinx + C#

Explanation:

The quotient rule is a formula for finding the derivative of #u/v#, rather than the integral of #u/v#. There is no formula for finding integral of #u/v#

The integral you have specified can be deal with as follows;

# int sinx/tanx dx = int sinx/(sinx/cosx) dx #

# :. int sinx/tanx dx = int sinx * (cosx/sinx) dx #

# :. int sinx/tanx dx = int cosx dx #

# :. int sinx/tanx dx = sinx + C#

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