What is the integral of (x^{1.5}+9x^{3.5}) ?

The integral of (x^{1.5}+9x^{3.5}) is 0.4x^{2.5}+2x^{4.5}+C

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integral of (x^{1.5}+9x^{3.5})

\int (x^{1.5} + 9 x^{3.5}) d x

0.4 x^{2.5} + 2 x^{4.5} + C

Solution steps

\int x^{1.5} + 9 x^{3.5} 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 x^{1.5} d x + \int 9 x^{3.5} d x

\int x^{1.5} d x = 0.4 x^{2.5}

\int 9 x^{3.5} d x = 2 x^{4.5}

= 0.4 x^{2.5} + 2 x^{4.5}

Add a constant to the solution

= 0.4 x^{2.5} + 2 x^{4.5} + C

(7 x + 2 y) \frac{d y}{d x} = - 2 x - 7 y

x \to 2 + lim (\frac{x + 4}{x - 2})

x \to 0 lim (\frac{7 x}{∣ x ∣})

x \to 1 - lim (ln (x^{2} - 1))

x \to 6 + lim (\frac{7}{x - 6})

What is the integral of (x^{1.5}+9x^{3.5}) ?
The integral of (x^{1.5}+9x^{3.5}) is 0.4x^{2.5}+2x^{4.5}+C