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

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

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

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

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

Solution steps

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

\int 5 x^{3} d x = \frac{5 x ^{4}}{4}

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

\int \frac{1}{9 y ^{2} + 6 y + 5} d y

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

\int - \frac{6}{7 x 49 x ^{2} - 25} d x

\int \frac{( y ^{3} - y ^{2} + 1 )}{( y ^{2} + 2 y + 2 ) ^{2}} d y

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