What is the integral of (2picos(pix)) ?

The integral of (2picos(pix)) is 2sin(pix)+C

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integral of (2picos(pix))

\int (2 π cos (π x)) d x

2 sin (π x) + C

Solution steps

\int 2 π cos (π x) d x

Take the constant out:

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

= 2 π \cdot \int cos (π x) d x

Apply u-substitution

: \int cos (u) \frac{1}{π} d u

= 2 π \cdot \int 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

= 2 π \frac{1}{π} \cdot \int cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= 2 π \frac{1}{π} sin (u)

Substitute back

u = π x

= 2 π \frac{1}{π} sin (π x)

Simplify

2 π \frac{1}{π} sin (π x) : 2 sin (π x)

= 2 sin (π x)

Add a constant to the solution

= 2 sin (π x) + C

\int - sin (x) cos (x) d x

\int \frac{e ^{3}}{x} d x

x \to 0 lim (\frac{∣ x ∣}{4 x})

\frac{d ^{2} y}{d x ^{2}} - 12 \frac{d y}{d x} + 36 y = 0

What is the integral of (2picos(pix)) ?
The integral of (2picos(pix)) is 2sin(pix)+C