What is the integral from 2 to x^2 of cos(x^2+1) ?

The integral from 2 to x^2 of cos(x^2+1) is

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integral from 2 to x^2 of cos(x^2+1)

\int_{2}^{x^{2}} cos (x^{2} + 1) d x

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

Solution steps

\int_{2}^{x^{2}} cos (x^{2} + 1) d x

Rewrite using trig identities

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

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

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

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

\int_{0}^{2 π} x^{2} sin (2 x) d x

\frac{d}{d t} (3 sin (3 t))

(\frac{2 y}{x} + 2 x) + (2 ln (x) - 3) y^{^{'}} = 0

\frac{\partial}{\partial x} (\frac{26 x ^{2}}{( x - y ) ^{2}})

1 + 4 x^{2} - 2 x^{3}

What is the integral from 2 to x^2 of cos(x^2+1) ?
The integral from 2 to x^2 of cos(x^2+1) is