- #1

jkristia

- 54

- 0

## Homework Statement

I'm trying to do an integration by substitution, but I'm completely stuck at the moment

∫(1-sin

^{2}θ)cosθ dθ

## Homework Equations

*∫u dv = uv - ∫v du*

## The Attempt at a Solution

*u*= 1 - sin

^{2}θ

*dv*= cosθ dθ

*du*= -2sinθcosθ or -sin(2θ)

*v*= sin

I found

*du*as the derivative of (1 - sin

^{2})

= 0 - 2(sin)(cos) = -2sinθcosθ

Now when I insert I get

(1 - sin

^{2}θ)(sinθ) - ∫(sinθ)(-2sinθcosθ)

sinθ-sin

^{3}θ - ∫-2 sin

^{2}θcosθ

sinθ-sin

^{3}θ - (-2) ∫sin

^{2}θcosθ

sinθ-sin

^{3}θ - (-2) ∫(1-cos

^{2}θ)cosθ

sinθ-sin

^{3}θ - (-2) ∫cosθ-cos

^{3}θ

I think I'm on the wrong track here.

Where did I go wrong? - any help is much appreciated.

Thanks