What is the integral of cos(x^2-5) ?

The integral of cos(x^2-5) is cos(5)sqrt(pi/2)\C(sqrt(2/pi)x)+sin(5)sqrt(pi/2)\S(sqrt(2/pi)x)+C

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integral of cos(x^2-5)

\int cos (x^{2} - 5) d x

cos (5) \frac{π}{2} C (\frac{2}{π} x) + sin (5) \frac{π}{2} § (\frac{2}{π} x) + C

Solution steps

\int cos (x^{2} - 5) d x

Rewrite using trig identities

= \int cos (x^{2}) cos (5) + sin (x^{2}) sin (5) 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}) cos (5) d x + \int sin (x^{2}) sin (5) d x

\int cos (x^{2}) cos (5) d x = cos (5) \frac{π}{2} C (\frac{2}{π} x)

\int sin (x^{2}) sin (5) d x = sin (5) \frac{π}{2} § (\frac{2}{π} x)

= cos (5) \frac{π}{2} C (\frac{2}{π} x) + sin (5) \frac{π}{2} § (\frac{2}{π} x)

Add a constant to the solution

= cos (5) \frac{π}{2} C (\frac{2}{π} x) + sin (5) \frac{π}{2} § (\frac{2}{π} x) + C

x \to 2 lim (\frac{3 ^{x}}{x + 1})

\int x e^{x + 1} d x

\int sec^{3} (v) d v

\frac{\partial}{\partial x} (x sec (y))

y^{^{'}} = \frac{cot ( y )}{t}

What is the integral of cos(x^2-5) ?
The integral of cos(x^2-5) is cos(5)sqrt(pi/2)\C(sqrt(2/pi)x)+sin(5)sqrt(pi/2)\S(sqrt(2/pi)x)+C