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

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

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

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

6 cos (x) + 7 sin (x) + C

Solution steps

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

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

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

= - (- 6 cos (x)) + 7 sin (x)

Simplify

= 6 cos (x) + 7 sin (x)

Add a constant to the solution

= 6 cos (x) + 7 sin (x) + C

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