What is the integral of (2ti+j+k) ?

The integral of (2ti+j+k) is it^2+jt+kt+C

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integral of (2ti+j+k)

\int (2 t i + j + k) d t

i t^{2} + j t + k t + C

Solution steps

\int 2 t i + j + k 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 i d t + \int j d t + \int k d t

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

\int j d t = j t

\int k d t = k t

= i t^{2} + j t + k t

Add a constant to the solution

= i t^{2} + j t + k t + C