- #1
juantheron
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$\displaystyle \int \frac{1}{\sqrt{\sin 2x}}dx$
jacks said:$\displaystyle \int \frac{1}{\sqrt{\sin 2x}}dx$
An indefinite integral is an antiderivative of a function. It is a mathematical operation that reverses the process of differentiation, and gives a family of functions that differ by a constant.
To solve an indefinite integral, you need to use the techniques of integration, such as substitution, integration by parts, or trigonometric substitutions. You also need to know the basic rules of integration, such as the power rule and the constant multiple rule.
The general formula for indefinite integrals is ∫f(x)dx = F(x) + C, where F(x) is the antiderivative of f(x) and C is the constant of integration.
To integrate a function with a square root in the denominator, you can use the substitution method, where you replace the square root with a new variable and then solve the resulting integral. In some cases, you may also need to use trigonometric substitutions.
The indefinite integral of $\frac{1}{\sqrt{\sin 2x}}$ is given by $\int \frac{1}{\sqrt{\sin 2x}}dx = \frac{1}{\sqrt{2}}\arctan \left( \sqrt{\frac{\sin 2x}{\cos 2x}} \right) + C$, where C is the constant of integration.