What is the integral of e^{sin(pix)}cos(pix) ?

The integral of e^{sin(pix)}cos(pix) is 1/pi e^{sin(pix)}+C

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integral of e^{sin(pix)}cos(pix)

\int e^{s i n (π x)} cos (π x) d x

\frac{1}{π} e^{s i n (π x)} + C

Solution steps

\int e^{s i n (π x)} cos (π x) d x

Apply u-substitution

: \int e^{s i n (u)} cos (u) \frac{1}{π} d u

= \int e^{s i n (u)} cos (u) \frac{1}{π} d u

Take the constant out:

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

= \frac{1}{π} \cdot \int e^{s i n (u)} cos (u) d u

Apply u-substitution

: \int e^{v} d v

= \frac{1}{π} \cdot \int e^{v} d v

Use the common integral:

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

= \frac{1}{π} e^{v}

Substitute back

= \frac{1}{π} e^{s i n (π x)}

Add a constant to the solution

= \frac{1}{π} e^{s i n (π x)} + C

\int_{0}^{3} \frac{- 6}{x x} d x

(1 - 5 y + x) y^{^{'}} + y = 5 x - 1

(\frac{1}{x})^{^{'}}

\int 9 x cos (x) d x

\frac{d y}{d x} = \frac{1}{y}

What is the integral of e^{sin(pix)}cos(pix) ?
The integral of e^{sin(pix)}cos(pix) is 1/pi e^{sin(pix)}+C