What is the integral of pcos((pix)/(2l)) ?

The integral of pcos((pix)/(2l)) is p(2l)/pi sin((xpi)/(2l))+C

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integral of pcos((pix)/(2l))

\int p cos (\frac{π x}{2 l}) d x

p \frac{2 l}{π} sin (\frac{x π}{2 l}) + C

Solution steps

\int p cos (\frac{π x}{2 l}) d x

Take the constant out:

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

= p \cdot \int cos (\frac{x π}{2 l}) d x

Apply u-substitution

: \int \frac{2 l cos ( u )}{π} d u

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

Take the constant out:

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

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

Use the common integral:

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

= p \frac{2 l}{π} sin (u)

Substitute back

u = \frac{x π}{2 l}

= p \frac{2 l}{π} sin (\frac{x π}{2 l})

Add a constant to the solution

= p \frac{2 l}{π} sin (\frac{x π}{2 l}) + C

x \to 1 - lim (\frac{3}{∣ x - 1 ∣})

\frac{\partial}{\partial x} (3 x^{\frac{1}{2}})

\int \frac{1}{( 9 + x ^{2} ) ^{3}} d x

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

y = 5 - x^{2}, y = x^{2} + 3

What is the integral of pcos((pix)/(2l)) ?
The integral of pcos((pix)/(2l)) is p(2l)/pi sin((xpi)/(2l))+C