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

The integral of sin(x^2)+cos(2x)-1/2 is sqrt(pi/2)\S(sqrt(2/pi)x)+1/2 sin(2x)-1/2 x+C

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

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

\frac{π}{2} § (\frac{2}{π} x) + \frac{1}{2} sin (2 x) - \frac{1}{2} x + C

Solution steps

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

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

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

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

= \frac{π}{2} § (\frac{2}{π} x) + \frac{1}{2} sin (2 x) - \frac{1}{2} x

Add a constant to the solution

= \frac{π}{2} § (\frac{2}{π} x) + \frac{1}{2} sin (2 x) - \frac{1}{2} x + C

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What is the integral of sin(x^2)+cos(2x)-1/2 ?
The integral of sin(x^2)+cos(2x)-1/2 is sqrt(pi/2)\S(sqrt(2/pi)x)+1/2 sin(2x)-1/2 x+C