What is the integral of 1/(sqrt(x)cos(1-\sqrt{x))} ?

The integral of 1/(sqrt(x)cos(1-\sqrt{x))} is 2sec(1)sqrt(x)+C

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integral of 1/(sqrt(x)cos(1-\sqrt{x))}

\int \frac{1}{x cos ( 1 - x )} d x

2 sec (1) x + C

Solution steps

\int \frac{1}{x cos ( 1 - x )} d x

Apply exponent rule:

\frac{1}{a ^{b}} = a^{- b}

\frac{1}{x cos ( 1 - x )} = x^{- \frac{1}{2}} \frac{1}{cos ( 1 - )}

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

Take the constant out:

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

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

Apply the Power Rule

: 2 x^{\frac{1}{2}}

= \frac{1}{cos ( 1 )} \cdot 2 x^{\frac{1}{2}}

Simplify

\frac{1}{cos ( 1 )} \cdot 2 x^{\frac{1}{2}} : 2 sec (1) x

= 2 sec (1) x

Add a constant to the solution

= 2 sec (1) x + C

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What is the integral of 1/(sqrt(x)cos(1-\sqrt{x))} ?
The integral of 1/(sqrt(x)cos(1-\sqrt{x))} is 2sec(1)sqrt(x)+C