Solving an Integral with 17sin^3(cos^5)d(theta) Using Trigonometric Substitution

[tangibleLime]

Homework Statement

$$\int 17sin^3(\theta)cos^5(\theta)d\theta$$

Homework Equations

The Attempt at a Solution

$$\int 17sin^3(\theta)cos^5(\theta)d\theta$$

Pulling out constant, breaking up the sin^3.
$$17 \int sin^2(\theta)cos^5(\theta)sin(\theta)d\theta$$

Using the trig identity to replace the sin^2
$$17 \int (1-cos^2(\theta))cos^5(\theta)sin(\theta)d\theta$$

Using u-subs to get rid of the other sin.
$$u = cos(\theta), du = sin(\theta)d\theta$$
$$17 \int (1-u^2)u^5 du$$

$$17 \int u^5-u^7 du$$

$$17[\frac{u^6}{6}-\frac{u^8}{8}]$$

Subbing back in for u.
$$17[\frac{cos^6\theta}{6}-\frac{cos^8\theta}{8}]$$

Homework software says incorrect. Any hints would be great!

 

[╔(σ_σ)╝]

du = -sinx not sinx :-)

 

[tangibleLime]

Cripes, thanks. 0_0

 

[╔(σ_σ)╝]

np :-)