What is the integral of 16cos^4(5pi)t ?

The integral of 16cos^4(5pi)t is 8t^2+C

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integral of 16cos^4(5pi)t

\int 16 cos^{4} (5 π) t d t

8 t^{2} + C

Solution steps

\int 16 cos^{4} (5 π) t d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 16 cos^{4} (5 π) \cdot \int t d t

16 cos^{4} (5 π) = 16

= 16 \cdot \int t d t

Apply the Power Rule

= 16 \cdot \frac{t ^{2}}{2}

Simplify

16 \cdot \frac{t ^{2}}{2} : 8 t^{2}

= 8 t^{2}

Add a constant to the solution

= 8 t^{2} + C