What is the integral of 1/(\sqrt[4]{1+x)} ?

The integral of 1/(\sqrt[4]{1+x)} is 4/3 (1+x)^{3/4}+C

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integral of 1/(\sqrt[4]{1+x)}

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

\frac{4}{3} (1 + x)^{\frac{3}{4}} + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{4 u} d u

= \int \frac{1}{4 u} d u

Apply the Power Rule

: \frac{4}{3} u^{\frac{3}{4}}

= \frac{4}{3} u^{\frac{3}{4}}

Substitute back

u = 1 + x

= \frac{4}{3} (1 + x)^{\frac{3}{4}}

Add a constant to the solution

= \frac{4}{3} (1 + x)^{\frac{3}{4}} + C

\int \frac{1}{( a ^{2} + x ^{2} ) ^{\frac{5}{2}}} d x

\frac{d}{d a} (b lo g_{10} (\frac{y}{x} + \frac{0.6 x}{a}))

y = x^{\frac{4}{3}}, y = 2 x^{\frac{1}{3}}

\int \frac{x}{6} d x

(arctan (3 x))^{2}

What is the integral of 1/(\sqrt[4]{1+x)} ?
The integral of 1/(\sqrt[4]{1+x)} is 4/3 (1+x)^{3/4}+C