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

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

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

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

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

Solution steps

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

\int 1 d x = x

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

= x + 2 π § (\frac{2}{π} \frac{x}{2})

Add a constant to the solution

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

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