What is the integral of e^{(pix)/4} ?

The integral of e^{(pix)/4} is 4/pi e^{(pix)/4}+C

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integral of e^{(pix)/4}

\int e^{\frac{π x}{4}} d x

\frac{4}{π} e^{\frac{π x}{4}} + C

Solution steps

\int e^{\frac{π x}{4}} d x

Apply u-substitution

: \int e^{u} \frac{4}{π} d u

= \int e^{u} \frac{4}{π} d u

Take the constant out:

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

= \frac{4}{π} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{4}{π} e^{u}

Substitute back

u = \frac{π x}{4}

= \frac{4}{π} e^{\frac{π x}{4}}

Add a constant to the solution

= \frac{4}{π} e^{\frac{π x}{4}} + C

x \to 3 + lim (\frac{ln ( x )}{x - 3})

\int \frac{1}{x ^{2} + 12 x} d x

y^{^{'}} = 25 + y^{2}

\frac{s + 2}{( s ^{2} + 4 )}

\frac{d}{d t} (\frac{1}{3} t^{3})

What is the integral of e^{(pix)/4} ?
The integral of e^{(pix)/4} is 4/pi e^{(pix)/4}+C