What is the integral of 3t^2+2t+2 ?

The integral of 3t^2+2t+2 is t^3+t^2+2t+C

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integral of 3t^2+2t+2

integral

3 t^{2} + 2 t + 2

t^{3} + t^{2} + 2 t + C

Solution steps

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

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

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

\int 2 d t = 2 t

= t^{3} + t^{2} + 2 t

Add a constant to the solution

= t^{3} + t^{2} + 2 t + C

\frac{2}{( - x ^{2} + 2 x + 1 )}

\frac{( a ^{2} - x ^{2} ) ^{3}}{2}

\frac{sinh ( x )}{( 1 + cosh ^{2} ( x ) )}

\frac{1}{( 1 + t ) ^{4}}

\frac{x ^{3}}{( x ^{2} - 1 ) ^{3}}