What is the integral of 1+x^{4/5} ?

The integral of 1+x^{4/5} is x+5/9 x^{9/5}+C

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integral of 1+x^{4/5}

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

x + \frac{5}{9} x^{\frac{9}{5}} + C

Solution steps

\int 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

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

\int 1 d x = x

\int x^{\frac{4}{5}} d x = \frac{5}{9} x^{\frac{9}{5}}

= x + \frac{5}{9} x^{\frac{9}{5}}

Add a constant to the solution

= x + \frac{5}{9} x^{\frac{9}{5}} + C

y = \frac{1 - x ^{2}}{( 1 + x ^{2} ) ^{2}}

f (x) = 1 - 2 x

5 \frac{d y}{d x} + 25 x^{4} y = 5 x^{4}, y (0) = - 7

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

c \to 1 lim (δ (x - c))

What is the integral of 1+x^{4/5} ?
The integral of 1+x^{4/5} is x+5/9 x^{9/5}+C