What is the integral of (\sqrt[m]{x}-1)/(\sqrt[m]{x)} ?

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

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integral of (\sqrt[m]{x}-1)/(\sqrt[m]{x)}

x - \frac{m x ^{\frac{- 1 + m}{m}}}{- 1 + m} + C

Solution steps

Expand

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 = x

= x - \frac{m x ^{\frac{- 1 + m}{m}}}{- 1 + m}

Add a constant to the solution

= x - \frac{m x ^{\frac{- 1 + m}{m}}}{- 1 + m} + C

5 cos (9 x), 5 - 5 cos (9 x)

f (x) = 8 sin^{6} (x)

x \to 4 + lim (\frac{1}{∣ 4 - x ∣})

\int t - 4 cos (t) d t

y = x^{3}, at x = 5

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