What is the integral of-5pisin(pix) ?

The integral of-5pisin(pix) is 5cos(pix)+C

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integral of-5pisin(pix)

\int - 5 π sin (π x) d x

5 cos (π x) + C

Solution steps

\int - 5 π sin (π x) d x

Take the constant out:

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

= - 5 π \cdot \int sin (π x) d x

Apply u-substitution

: \int sin (u) \frac{1}{π} d u

= - 5 π \cdot \int sin (u) \frac{1}{π} d u

Take the constant out:

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

= - 5 π \frac{1}{π} \cdot \int sin (u) d u

Use the common integral:

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

= - 5 π \frac{1}{π} (- cos (u))

Substitute back

u = π x

= - 5 π \frac{1}{π} (- cos (π x))

Simplify

- 5 π \frac{1}{π} (- cos (π x)) : 5 cos (π x)

= 5 cos (π x)

Add a constant to the solution

= 5 cos (π x) + C

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

- \frac{2}{x ^{3}}

\frac{d}{d x} (\frac{x}{x - 9})

\int \frac{( 8 x - 3 )}{12 x - 4 x ^{2} - 5} d x

y = - 2 - 7 x^{2}

What is the integral of-5pisin(pix) ?
The integral of-5pisin(pix) is 5cos(pix)+C