Find the indefinite integral. (Use C for the constant of integration.) integral sin^4 5 theta d...

Question:

Find the indefinite integral. (Use C for the constant of integration.)

{eq}\displaystyle \int \sin^4 5 \theta\ d \theta {/eq}.

Indefinite Integral:

Assume that {eq}v {/eq} is a single-valued function of {eq}x {/eq} and {eq}K {/eq} is an anti derivative of {eq}v {/eq} such that {eq}\displaystyle v\left( x \right) = K'\left( x \right),\;\forall \;x {/eq}.

Then the indefinite integral of {eq}\displaystyle v {/eq} is defined as {eq}\displaystyle \int v\left( x \right)dx = K\left( x \right) + C {/eq}, where {eq}c {/eq} is an integration constant.

Answer and Explanation: 1

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Given that: {eq}\displaystyle \int {{{\sin }^4}} 5\theta d\theta {/eq}

{eq}\displaystyle\ \eqalign{ & \int {{{\left( {{{\sin }^2}5\theta }...

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