What is the integral of 21x^2-12x-5 ?

The integral of 21x^2-12x-5 is 7x^3-6x^2-5x+C

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integral of 21x^2-12x-5

\int 21 x^{2} - 12 x - 5 d x

7 x^{3} - 6 x^{2} - 5 x + C

Solution steps

\int 21 x^{2} - 12 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 21 x^{2} d x - \int 12 x d x - \int 5 d x

\int 21 x^{2} d x = 7 x^{3}

\int 12 x d x = 6 x^{2}

\int 5 d x = 5 x

= 7 x^{3} - 6 x^{2} - 5 x

Add a constant to the solution

= 7 x^{3} - 6 x^{2} - 5 x + C

\int \frac{x ^{2}}{x + 6} d x

\int t^{2} - 6 t + 8 d t

\int 4 e d x

\int x sin (w x) d x

What is the integral of 21x^2-12x-5 ?
The integral of 21x^2-12x-5 is 7x^3-6x^2-5x+C