What is the integral from sqrt(x) to x of sin(t^2-1) ?

The integral from sqrt(x) to x of sin(t^2-1) is

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integral from sqrt(x) to x of sin(t^2-1)

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

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

Solution steps

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

Rewrite using trig identities

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

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

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

\int_{2}^{4} - x + 4 d x

\int_{1}^{e} x^{9} ln (x) d x

\int_{0}^{π} - sin (t) cos (t) d t

\int_{e}^{- 2 x} 1 d x

\int_{- 5}^{0} 2 x - x^{2} - 7 x d x

What is the integral from sqrt(x) to x of sin(t^2-1) ?
The integral from sqrt(x) to x of sin(t^2-1) is