What is the integral of 5\sqrt[4]{e^x} ?

The integral of 5\sqrt[4]{e^x} is 20e^{x/4}+C

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integral of 5\sqrt[4]{e^x}

\int 5 4 e^{x} d x

20 e^{\frac{x}{4}} + C

Solution steps

\int 5 4 e^{x} d x

Take the constant out:

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

= 5 \cdot \int 4 e^{x} d x

Apply radical rule:

n a^{m} = a^{\frac{m}{n}},

assuming

a \geq 0

= 5 \cdot \int e^{\frac{x}{4}} d x

Apply u-substitution

= 5 \cdot \int e^{u} \cdot 4 d u

Take the constant out:

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

= 5 \cdot 4 \cdot \int e^{u} d u

Use the common integral:

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

= 5 \cdot 4 e^{u}

Substitute back

u = \frac{x}{4}

= 5 \cdot 4 e^{\frac{x}{4}}

Simplify

= 20 e^{\frac{x}{4}}

Add a constant to the solution

= 20 e^{\frac{x}{4}} + C

t a y l or 2^{x}

\int \frac{x ^{2} + 48 x - 16}{x ^{3} - 16 x} d x

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

\frac{d y}{d t} = - \frac{y}{t ^{2}}

t an g e n t f (x) = 6 x - x^{2}, at x = 4

What is the integral of 5\sqrt[4]{e^x} ?
The integral of 5\sqrt[4]{e^x} is 20e^{x/4}+C