What is the integral of 3t^2-10t+19 ?

The integral of 3t^2-10t+19 is t^3-5t^2+19t+C

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integral of 3t^2-10t+19

\int 3 t^{2} - 10 t + 19 d t

t^{3} - 5 t^{2} + 19 t + C

Solution steps

\int 3 t^{2} - 10 t + 19 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 3 t^{2} d t - \int 10 t d t + \int 19 d t

\int 3 t^{2} d t = t^{3}

\int 10 t d t = 5 t^{2}

\int 19 d t = 19 t

= t^{3} - 5 t^{2} + 19 t

Add a constant to the solution

= t^{3} - 5 t^{2} + 19 t + C

\int \frac{3 x ^{2} + 1}{x ^{3} + x ^{2} + x + 1} d x

\int 3^{2 x} (2^{1 - x} + 1) d x

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\int 5 (sin (x))^{4} d x

What is the integral of 3t^2-10t+19 ?
The integral of 3t^2-10t+19 is t^3-5t^2+19t+C