Solve \int \pi /40 sinx cos3x dx

Evaluate

\int \frac{π}{40} sin (x) cos (3 x) d x

Use the property of integral \int k f (x) d x = k \int f (x) d x

\frac{π}{40} \times \int sin (x) cos (3 x) d x

Use the property of integral \int sin (a x) cos (b x) d x = - \frac{cos (( a + b ) x )}{2 ( a + b )} - \frac{cos (( a - b ) x )}{2 ( a - b )}, a^{2} \neq = b^{2}

\frac{π}{40} (- \frac{cos ( ( 1 + 3 ) x )}{2 ( 1 + 3 )} - \frac{cos ( ( 1 - 3 ) x )}{2 ( 1 - 3 )})

Simplify

More Steps

\frac{π}{40} (- \frac{1}{8} cos (4 x) + \frac{1}{4} cos (2 x))

Use the the distributive property to expand the expression

\frac{π}{40} (- \frac{1}{8} cos (4 x)) + \frac{π}{40} \times \frac{1}{4} cos (2 x)

Multiply the terms

More Steps

- \frac{π}{320} cos (4 x) + \frac{π}{40} \times \frac{1}{4} cos (2 x)

Multiply the terms

More Steps

- \frac{π}{320} cos (4 x) + \frac{π}{160} cos (2 x)

Solution

- \frac{π}{320} cos (4 x) + \frac{π}{160} cos (2 x) + C, C \in R

Evaluate the integral