What is the integral of (5x^4-8x^3+9x^2-2x+7) ?

The integral of (5x^4-8x^3+9x^2-2x+7) is x^5-2x^4+3x^3-x^2+7x+C

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integral of (5x^4-8x^3+9x^2-2x+7)

\int (5 x^{4} - 8 x^{3} + 9 x^{2} - 2 x + 7) d x

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

Solution steps

\int 5 x^{4} - 8 x^{3} + 9 x^{2} - 2 x + 7 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^{4} d x - \int 8 x^{3} d x + \int 9 x^{2} d x - \int 2 x d x + \int 7 d x

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

\int 8 x^{3} d x = 2 x^{4}

\int 9 x^{2} d x = 3 x^{3}

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

\int 7 d x = 7 x

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

Add a constant to the solution

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

y^{^{'}} = y^{5}

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

x \to 0 lim ((sin (\frac{x}{2}))^{x})

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

\int 4^{t} d t

What is the integral of (5x^4-8x^3+9x^2-2x+7) ?
The integral of (5x^4-8x^3+9x^2-2x+7) is x^5-2x^4+3x^3-x^2+7x+C