What is the integral of (2sin(x)-3cos(x)+1/2) ?

The integral of (2sin(x)-3cos(x)+1/2) is -2cos(x)-3sin(x)+1/2 x+C

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integral of (2sin(x)-3cos(x)+1/2)

\int (2 sin (x) - 3 cos (x) + \frac{1}{2}) d x

- 2 cos (x) - 3 sin (x) + \frac{1}{2} x + C

Solution steps

\int 2 sin (x) - 3 cos (x) + \frac{1}{2} 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 2 sin (x) d x - \int 3 cos (x) d x + \int \frac{1}{2} d x

\int 2 sin (x) d x = - 2 cos (x)

\int 3 cos (x) d x = 3 sin (x)

\int \frac{1}{2} d x = \frac{1}{2} x

= - 2 cos (x) - 3 sin (x) + \frac{1}{2} x

Add a constant to the solution

= - 2 cos (x) - 3 sin (x) + \frac{1}{2} x + C

\int csc^{2} (t) d t

\frac{2}{( s + 3 ) ^{2} - 9}

\int csc^{2} (5 y) d y

y = \frac{1}{x}, y = \frac{1}{x ^{2}}, x = 3

\frac{d}{d x} (x sin (x))

What is the integral of (2sin(x)-3cos(x)+1/2) ?
The integral of (2sin(x)-3cos(x)+1/2) is -2cos(x)-3sin(x)+1/2 x+C