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

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

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integral of (e^{\sqrt[4]{x}})/(sqrt(x))

Solution steps

Apply u-substitution

: \int 4 e^{u} u d u

= \int 4 e^{u} u d u

Take the constant out:

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

= 4 \cdot \int e^{u} u d u

Apply Integration By Parts

: e^{u} u - \int e^{u} d u

= 4 (e^{u} u - \int e^{u} d u)

\int e^{u} d u = e^{u}

= 4 (e^{u} u - e^{u})

Substitute back

Add a constant to the solution

\int \frac{e ^{- x}}{e ^{- 2 x} + 1} d x

\int 2 (2 x + 3)^{3} d x

\int \frac{x ^{2} - 2 x + 3}{x} d x

\int \frac{9}{2 - 3 x} d x

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