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

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

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integral of sin(x^2-1)

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

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

Solution steps

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

Rewrite using trig identities

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

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

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

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{e ^{x}}{1 - e ^{x}})

\int \frac{5 x ^{2} - x + 17}{( x + 2 ) ( x ^{2} + 9 )} d x

\frac{d y}{d x} = e^{8 x + y}

f (x) = csc (x + 5)

\frac{d}{d x} (ln (\frac{5 x + 2}{5 x - 2}))

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