# Evaluate the integral. (Use C for the constant of integration.) Integral of (cos theta)(cos^5(sin...

## Question:

Evaluate the integral. (Use {eq}C {/eq} for the constant of integration.)

{eq}\int (\cos \theta)(\cos^5 (\sin \theta)) \; \mathrm{d} \theta {/eq}

## Integration by Substitution:

With the help of integration by substitution, we can convert a difficult integral to an easier integral. This has the effect of changing the variable and the integrand. When dealing with definite integrals, the limits of integration can also change. For example, if we have to integrate the following function:

{eq}\displaystyle{ \int f ( g ( x ) ) g ^ { \prime } ( x ) d x }{/eq}

then we can substitute {eq}\displaystyle{ u=g(x) }{/eq} and can transform the integral into:

{eq}\displaystyle{ \int f ( u ) d u }{/eq}

which look apparently easy as compared to the previous one. We can use the substitution method as many times as required in the same problem.

Become a Study.com member to unlock this answer!

We have,

{eq}\displaystyle{ \int (\cos \theta)(\cos^5 (\sin \theta)) \; \mathrm{d} \theta }{/eq}

We can rewrite this as:

{eq}\displaystyle{ \int...