What is the integral of (5x^2-4x+3) ?

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

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integral of (5x^2-4x+3)

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

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

Solution steps

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

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

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

\int 3 d x = 3 x

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

Add a constant to the solution

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

\int 19 t e^{t} d t

\int \frac{4}{x ^{\frac{1}{3}} + x ^{\frac{1}{2}}} d x

\int (x^{\frac{1}{3}} - x + 1) d x

\int \frac{1}{x ^{2} + 121} d x

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