What is the integral of (5x^3+2x^2-2x+1) ?

The integral of (5x^3+2x^2-2x+1) is (5x^4)/4+(2x^3)/3-x^2+x+C

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integral of (5x^3+2x^2-2x+1)

\int (5 x^{3} + 2 x^{2} - 2 x + 1) d x

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

Solution steps

\int 5 x^{3} + 2 x^{2} - 2 x + 1 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 2 x^{2} d x - \int 2 x d x + \int 1 d x

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

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

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

\int 1 d x = x

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

Add a constant to the solution

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

\frac{x}{( 1 - x ^{2} ) ^{\frac{1}{2}}}

\frac{d}{d x} (\frac{2 π}{x})

f (x) = (3 x + 1)^{\frac{1}{2}}

\int x + 5 d x

sec^{2} (π t)

What is the integral of (5x^3+2x^2-2x+1) ?
The integral of (5x^3+2x^2-2x+1) is (5x^4)/4+(2x^3)/3-x^2+x+C