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

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

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integral of 2t+sec^2(t)

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

t^{2} + tan (t) + C

Solution steps

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

\int 2 t d t = t^{2}

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

= t^{2} + tan (t)

Add a constant to the solution

= t^{2} + tan (t) + C

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