What is the integral of sin(26x)cos(17x) ?

The integral of sin(26x)cos(17x) is 1/2 (-1/43 cos(43x)-1/9 cos(9x))+C

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integral of sin(26x)cos(17x)

\int sin (26 x) cos (17 x) d x

\frac{1}{2} (- \frac{1}{43} cos (43 x) - \frac{1}{9} cos (9 x)) + C

Solution steps

\int sin (26 x) cos (17 x) d x

Use the following identity:

cos (t) sin (s) = \frac{sin ( s + t ) + sin ( s - t )}{2}

= \int \frac{sin ( 26 x + 17 x ) + sin ( 26 x - 17 x )}{2} d x

Take the constant out:

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

= \frac{1}{2} \cdot \int sin (26 x + 17 x) + sin (26 x - 17 x) d x

Simplify

= \frac{1}{2} \cdot \int sin (43 x) + sin (9 x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} (\int sin (43 x) d x + \int sin (9 x) d x)

\int sin (43 x) d x = - \frac{1}{43} cos (43 x)

\int sin (9 x) d x = - \frac{1}{9} cos (9 x)

= \frac{1}{2} (- \frac{1}{43} cos (43 x) - \frac{1}{9} cos (9 x))

Add a constant to the solution

= \frac{1}{2} (- \frac{1}{43} cos (43 x) - \frac{1}{9} cos (9 x)) + C

\int x sin (k x) d x

2 x e^{x^{2}}

\frac{\partial}{\partial x} (nani)

\frac{d y}{d x}, y = \frac{9}{x}

x \to - 1 lim (\frac{1}{x ^{2} + 2 x + 1})

What is the integral of sin(26x)cos(17x) ?
The integral of sin(26x)cos(17x) is 1/2 (-1/43 cos(43x)-1/9 cos(9x))+C