What is the integral of (ax^2+bx+c) ?

The integral of (ax^2+bx+c) is (ax^3)/3+(bx^2)/2+cx+C

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integral of (ax^2+bx+c)

\int (a x^{2} + b x + c) d x

\frac{a x ^{3}}{3} + \frac{b x ^{2}}{2} + c x + C

Solution steps

\int a x^{2} + b x + c 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 a x^{2} d x + \int b x d x + \int c d x

\int a x^{2} d x = \frac{a x ^{3}}{3}

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

\int c d x = c x

= \frac{a x ^{3}}{3} + \frac{b x ^{2}}{2} + c x

Add a constant to the solution

= \frac{a x ^{3}}{3} + \frac{b x ^{2}}{2} + c x + C

y = \frac{2 x - 1}{x + 2}

\frac{d}{d x} (x^{2} (ln (x)))

\frac{d}{d x} (ln (6 sec (x)))

f (x) = 2 x^{2} - 3 x + 1, 1, 2

y = 9 x, y = x^{2}

What is the integral of (ax^2+bx+c) ?
The integral of (ax^2+bx+c) is (ax^3)/3+(bx^2)/2+cx+C