What is the integral of ((-3x^3+\sqrt[5]{x}))/(5x) ?

The integral of ((-3x^3+\sqrt[5]{x}))/(5x) is -1/5 x^3+\sqrt[5]{x}+C

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integral of ((-3x^3+\sqrt[5]{x}))/(5x)

Solution steps

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

Expand

= \frac{1}{5} \cdot \int - 3 x^{2} + \frac{1}{x ^{\frac{4}{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

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

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

\int \frac{1}{x ^{\frac{4}{5}}} d x = 5 x^{\frac{1}{5}}

= \frac{1}{5} (- x^{3} + 5 x^{\frac{1}{5}})

Simplify

Add a constant to the solution

\frac{d}{d x} (e^{- ∣ x ∣})

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

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

y = 4 x^{2} - 1, y = 1 - 4 x^{2}

y^{'} = y (2 - y)

What is the integral of ((-3x^3+\sqrt[5]{x}))/(5x) ?
The integral of ((-3x^3+\sqrt[5]{x}))/(5x) is -1/5 x^3+\sqrt[5]{x}+C