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

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

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

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

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

Solution steps

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

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

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

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

Simplify

= 7 sin (x) + cos (x)

Add a constant to the solution

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

\int π t cos (\frac{π t}{2}) d t

\int (7 x + 2) d x

\int tan (x) sec^{2} (d) x d x

\int (π - x) cos (x) d x

\int 3 x^{2} y e^{3 x} d x

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