What is the integral of 2cos(x)+2sin(x) ?

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

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integral of 2cos(x)+2sin(x)

\int 2 cos (x) + 2 sin (x) d x

2 sin (x) - 2 cos (x) + C

Solution steps

\int 2 cos (x) + 2 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 2 cos (x) d x + \int 2 sin (x) d x

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

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

= 2 sin (x) - 2 cos (x)

Add a constant to the solution

= 2 sin (x) - 2 cos (x) + C

\int x^{2} (4 x^{3} - 3)^{8} d x

\int \frac{1}{x ^{2} + 4 x + 2} d x

\int x^{2} (cos (x)) d x

\int \frac{cos ( t )}{( 4 sin ( t ) + 12 ) ^{2}} d t

\int \frac{2 t - 4 + 9 t}{t} d t

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