What is the integral of cos(8x^2) ?

The integral of cos(8x^2) is (sqrt(pi))/4 \C((2*2x)/(sqrt(pi)))+C

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integral of cos(8x^2)

\int cos (8 x^{2}) d x

\frac{π}{4} C (\frac{2 \cdot 2 x}{π}) + C

Solution steps

\int cos (8 x^{2}) d x

Apply Integral Substitution

= \int \frac{1}{2} cos (2 u^{2}) d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int cos (2 u^{2}) d u

Use the nonelementary integral:

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

= \frac{1}{2} \cdot \frac{π}{2} C (\frac{2 u}{π})

Substitute back

u = 2 x

= \frac{1}{2} \cdot \frac{π}{2} C (\frac{2 \cdot 2 x}{π})

Simplify

\frac{1}{2} \cdot \frac{π}{2} C (\frac{2 \cdot 2 x}{π}) : \frac{π}{4} C (\frac{2 \cdot 2 x}{π})

= \frac{π}{4} C (\frac{2 \cdot 2 x}{π})

Add a constant to the solution

= \frac{π}{4} C (\frac{2 \cdot 2 x}{π}) + C

\frac{\partial}{\partial x} (- x)

\int_{0}^{4} 2 x d x

\frac{\partial}{\partial x} (e^{4 x} cos (7 y))

\frac{d}{d y} (y^{- 1})

\frac{d}{d x} (x^{2} e^{x} - 3)

What is the integral of cos(8x^2) ?
The integral of cos(8x^2) is (sqrt(pi))/4 \C((2*2x)/(sqrt(pi)))+C