What is the integral of 9x^2-8x+5 ?

The integral of 9x^2-8x+5 is 3x^3-4x^2+5x+C

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integral of 9x^2-8x+5

\int 9 x^{2} - 8 x + 5 d x

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

Solution steps

\int 9 x^{2} - 8 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 9 x^{2} d x - \int 8 x d x + \int 5 d x

\int 9 x^{2} d x = 3 x^{3}

\int 8 x d x = 4 x^{2}

\int 5 d x = 5 x

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

Add a constant to the solution

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

\int (4 x^{3} + x^{2} - 8 x + 12) d x

\int \frac{1}{2 u ^{\frac{1}{2}}} d u

\int (x^{2} - 6 x + 8) (x - 3) d x

f (x) = \frac{5}{x}

\int \frac{4 ^{x + 2}}{5 ^{x - 1}} d x