What is the integral of 12x^3+6x^2+4x+5 ?

The integral of 12x^3+6x^2+4x+5 is 3x^4+2x^3+2x^2+5x+C

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integral of 12x^3+6x^2+4x+5

\int 12 x^{3} + 6 x^{2} + 4 x + 5 d x

3 x^{4} + 2 x^{3} + 2 x^{2} + 5 x + C

Solution steps

\int 12 x^{3} + 6 x^{2} + 4 x + 5 d x

Apply the Sum Rule:

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

= \int 12 x^{3} d x + \int 6 x^{2} d x + \int 4 x d x + \int 5 d x

\int 12 x^{3} d x = 3 x^{4}

\int 6 x^{2} d x = 2 x^{3}

\int 4 x d x = 2 x^{2}

\int 5 d x = 5 x

= 3 x^{4} + 2 x^{3} + 2 x^{2} + 5 x

Add a constant to the solution

= 3 x^{4} + 2 x^{3} + 2 x^{2} + 5 x + C

\int 5 - ∣ x ∣ d x

\int \frac{t}{e ^{- t}} d t

\int 4 sin (x) + 5 sinh (x) d x

\int \frac{2}{( t - 3 ) t ^{2} - 6 t + 5} d t

\int \frac{8}{3} cos^{3} (x) d x

What is the integral of 12x^3+6x^2+4x+5 ?
The integral of 12x^3+6x^2+4x+5 is 3x^4+2x^3+2x^2+5x+C