What is the integral of 1/(sec(x^2)) ?

The integral of 1/(sec(x^2)) is sqrt(pi/2)\C(sqrt(2/pi)x)+C

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integral of 1/(sec(x^2))

\int \frac{1}{sec ( x ^{2} )} d x

\frac{π}{2} C (\frac{2}{π} x) + C

Solution steps

\int \frac{1}{sec ( x ^{2} )} d x

Use the basic trigonometric identity:

\frac{1}{sec ( x )} = cos (x)

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

Use the nonelementary integral:

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

= \frac{π}{2} C (\frac{2}{π} x)

Add a constant to the solution

= \frac{π}{2} C (\frac{2}{π} x) + C

\int (e^{\frac{x}{a}} + 1)^{\frac{1}{3}} e^{\frac{x}{a}} d x

\int_{2}^{4} \frac{x ( 2 x - 3 )}{6} d x

x \to 1 - lim (\frac{8}{1 - x})

\int \frac{x ^{3} + 3 x ^{2} + 6 x + 5}{x ^{2} + x + 2} d x

f^{^{'}} (x) = ln (x)

What is the integral of 1/(sec(x^2)) ?
The integral of 1/(sec(x^2)) is sqrt(pi/2)\C(sqrt(2/pi)x)+C