What is the integral of sin(6x)-7sin(7x) ?

The integral of sin(6x)-7sin(7x) is -1/6 cos(6x)+cos(7x)+C

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integral of sin(6x)-7sin(7x)

\int sin (6 x) - 7 sin (7 x) d x

- \frac{1}{6} cos (6 x) + cos (7 x) + C

Solution steps

\int sin (6 x) - 7 sin (7 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

= \int sin (6 x) d x - \int 7 sin (7 x) d x

\int sin (6 x) d x = - \frac{1}{6} cos (6 x)

\int 7 sin (7 x) d x = - cos (7 x)

= - \frac{1}{6} cos (6 x) - (- cos (7 x))

Simplify

= - \frac{1}{6} cos (6 x) + cos (7 x)

Add a constant to the solution

= - \frac{1}{6} cos (6 x) + cos (7 x) + C

\frac{6}{x}, 3 x, \frac{x}{3}

\frac{d}{d x} (sec^{3} (2 x))

\int_{- 7}^{- 5} \frac{3}{( x + 6 ) ^{\frac{8}{11}}} d x

f (x) = 1 - tan (x), at x = - \frac{π}{4}

\int 7 e^{2 x} d x

What is the integral of sin(6x)-7sin(7x) ?
The integral of sin(6x)-7sin(7x) is -1/6 cos(6x)+cos(7x)+C