What is the integral of 12x^2-7x+5 ?

The integral of 12x^2-7x+5 is 4x^3-(7x^2)/2+5x+C

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integral of 12x^2-7x+5

\int 12 x^{2} - 7 x + 5 d x

4 x^{3} - \frac{7 x ^{2}}{2} + 5 x + C

Solution steps

\int 12 x^{2} - 7 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^{2} d x - \int 7 x d x + \int 5 d x

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

\int 7 x d x = \frac{7 x ^{2}}{2}

\int 5 d x = 5 x

= 4 x^{3} - \frac{7 x ^{2}}{2} + 5 x

Add a constant to the solution

= 4 x^{3} - \frac{7 x ^{2}}{2} + 5 x + C

\int \frac{t}{t ^{4} + 81} d t

a re a \frac{1}{x x ^{2} - 1}, x = \frac{2}{2}, x = 2

\frac{d}{d x} ((4 x^{2} + 2 x - 5) (x^{3} + 7 x + 4))

d er i v a t i v e \frac{4 u ^{2}}{( u ^{2} + u ) ^{3}}

d er i v a t i v e f (x) = a cos (2 x) + b sin (2 x)

What is the integral of 12x^2-7x+5 ?
The integral of 12x^2-7x+5 is 4x^3-(7x^2)/2+5x+C