What is the integral of cos(n)t ?

The integral of cos(n)t is 1/2 t^2cos(n)+C

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integral of cos(n)t

\int cos (n) t d t

\frac{1}{2} t^{2} cos (n) + C

Solution steps

\int cos (n) t d t

Take the constant out:

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

= cos (n) \cdot \int t d t

Apply the Power Rule

= cos (n) \frac{t ^{2}}{2}

Simplify

cos (n) \frac{t ^{2}}{2} : \frac{1}{2} t^{2} cos (n)

= \frac{1}{2} t^{2} cos (n)

Add a constant to the solution

= \frac{1}{2} t^{2} cos (n) + C