What is the integral of 4cos(t)+sec^2(t) ?

The integral of 4cos(t)+sec^2(t) is 4sin(t)+tan(t)+C

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integral of 4cos(t)+sec^2(t)

\int 4 cos (t) + sec^{2} (t) d t

4 sin (t) + tan (t) + C

Solution steps

\int 4 cos (t) + sec^{2} (t) d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 4 cos (t) d t + \int sec^{2} (t) d t

\int 4 cos (t) d t = 4 sin (t)

\int sec^{2} (t) d t = tan (t)

= 4 sin (t) + tan (t)

Add a constant to the solution

= 4 sin (t) + tan (t) + C

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What is the integral of 4cos(t)+sec^2(t) ?
The integral of 4cos(t)+sec^2(t) is 4sin(t)+tan(t)+C