What is the integral of (1-x^3+5x^5-3x^7) ?

The integral of (1-x^3+5x^5-3x^7) is x-(x^4)/4+(5x^6)/6-(3x^8)/8+C

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integral of (1-x^3+5x^5-3x^7)

\int (1 - x^{3} + 5 x^{5} - 3 x^{7}) d x

x - \frac{x ^{4}}{4} + \frac{5 x ^{6}}{6} - \frac{3 x ^{8}}{8} + C

Solution steps

\int 1 - x^{3} + 5 x^{5} - 3 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 1 d x - \int x^{3} d x + \int 5 x^{5} d x - \int 3 x^{7} d x

\int 1 d x = x

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

\int 5 x^{5} d x = \frac{5 x ^{6}}{6}

\int 3 x^{7} d x = \frac{3 x ^{8}}{8}

= x - \frac{x ^{4}}{4} + \frac{5 x ^{6}}{6} - \frac{3 x ^{8}}{8}

Add a constant to the solution

= x - \frac{x ^{4}}{4} + \frac{5 x ^{6}}{6} - \frac{3 x ^{8}}{8} + C

\frac{d}{d x} (80 π cos (10 π x))

\frac{\partial}{\partial x} (x^{6} + 5 x y^{9})

\frac{d}{d x} (\frac{8 x ^{3} - 2 x + 9}{x})

\frac{d}{d x} (\frac{1}{4 x ^{3} + 5 x ^{2} - 7 x + 8})

\int x (x^{2} + 3)^{7} d x

What is the integral of (1-x^3+5x^5-3x^7) ?
The integral of (1-x^3+5x^5-3x^7) is x-(x^4)/4+(5x^6)/6-(3x^8)/8+C