What is the integral of (3x^5-5x^9) ?

The integral of (3x^5-5x^9) is (x^6)/2-(x^{10})/2+C

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integral of (3x^5-5x^9)

\int (3 x^{5} - 5 x^{9}) d x

\frac{x ^{6}}{2} - \frac{x ^{10}}{2} + C

Solution steps

\int 3 x^{5} - 5 x^{9} 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 3 x^{5} d x - \int 5 x^{9} d x

\int 3 x^{5} d x = \frac{x ^{6}}{2}

\int 5 x^{9} d x = \frac{x ^{10}}{2}

= \frac{x ^{6}}{2} - \frac{x ^{10}}{2}

Add a constant to the solution

= \frac{x ^{6}}{2} - \frac{x ^{10}}{2} + C

x \to y lim (\frac{x ^{n} - y ^{n}}{x - y})

e^{5 x}, e^{7 x}, 1

\int 3 x \cdot e^{- 2 x} d x

\int \frac{x ^{2}}{x ^{2} + 16} d x

e^{x} \frac{d y}{d x} = e^{- y} + e^{- 2 x - y}

What is the integral of (3x^5-5x^9) ?
The integral of (3x^5-5x^9) is (x^6)/2-(x^{10})/2+C