What is the integral of (21pi)/2 cos((21pix)/2) ?

The integral of (21pi)/2 cos((21pix)/2) is sin((21pix)/2)+C

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integral of (21pi)/2 cos((21pix)/2)

\int \frac{21 π}{2} cos (\frac{21 π x}{2}) d x

sin (\frac{21 π x}{2}) + C

Solution steps

\int \frac{21 π}{2} cos (\frac{21 π x}{2}) d x

Take the constant out:

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

= \frac{21 π}{2} \cdot \int cos (\frac{21 π x}{2}) d x

Apply u-substitution

= \frac{21 π}{2} \cdot \int cos (u) \frac{2}{21 π} d u

Take the constant out:

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

= \frac{21 π}{2} \cdot \frac{2}{21 π} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{21 π}{2} \cdot \frac{2}{21 π} sin (u)

Substitute back

u = \frac{21 x π}{2}

= \frac{21 π}{2} \cdot \frac{2}{21 π} sin (\frac{21 x π}{2})

Simplify

\frac{21 π}{2} \cdot \frac{2}{21 π} sin (\frac{21 x π}{2}) : sin (\frac{21 π x}{2})

= sin (\frac{21 π x}{2})

Add a constant to the solution

= sin (\frac{21 π x}{2}) + C

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What is the integral of (21pi)/2 cos((21pix)/2) ?
The integral of (21pi)/2 cos((21pix)/2) is sin((21pix)/2)+C