What is the integral of 2cos(4x)+sin(1/2)x ?

The integral of 2cos(4x)+sin(1/2)x is 1/2 sin(4x)+1/2 sin(1/2)x^2+C

integral of 2cos(4x)+sin(1/2)x

\int 2 cos (4 x) + sin (\frac{1}{2}) x d x

\frac{1}{2} sin (4 x) + \frac{1}{2} sin (\frac{1}{2}) x^{2} + C

Solution steps

\int 2 cos (4 x) + sin (\frac{1}{2}) 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 (4 x) d x + \int sin (\frac{1}{2}) x d x

\int 2 cos (4 x) d x = \frac{1}{2} sin (4 x)

\int sin (\frac{1}{2}) x d x = \frac{1}{2} sin (\frac{1}{2}) x^{2}

= \frac{1}{2} sin (4 x) + \frac{1}{2} sin (\frac{1}{2}) x^{2}

Add a constant to the solution

= \frac{1}{2} sin (4 x) + \frac{1}{2} sin (\frac{1}{2}) x^{2} + C

\int arccos (cos (x)) d x

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

\int \frac{3 x ^{2} + 1}{1 + ( x ^{3} + x ) ^{2}} d x

\int \frac{x e ^{x}}{49 + e ^{x}} d x

\int x^{3} e^{n x} d x

What is the integral of 2cos(4x)+sin(1/2)x ?
The integral of 2cos(4x)+sin(1/2)x is 1/2 sin(4x)+1/2 sin(1/2)x^2+C