Final answer to the problem
$\frac{1}{2\sqrt{7}}\arcsin\left(2.6457513w\right)+\frac{2.6457513}{2\sqrt{7}}w\sqrt{1-7w^2}+C_0$
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Step-by-step Solution
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First, factor the terms inside the radical by $7$ for an easier handling
$\int\sqrt{7\left(\frac{1}{7}-w^2\right)}dw$
Learn how to solve intégrales avec radicaux problems step by step online.
$\int\sqrt{7\left(\frac{1}{7}-w^2\right)}dw$
Learn how to solve intégrales avec radicaux problems step by step online. Integrate int((1-7w^2)^(1/2))dw. First, factor the terms inside the radical by 7 for an easier handling. Taking the constant out of the radical. We can solve the integral \int\sqrt{7}\sqrt{\frac{1}{7}-w^2}dw by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of dw, we need to find the derivative of w. We need to calculate dw, we can do that by deriving the equation above.
Final answer to the problem
$\frac{1}{2\sqrt{7}}\arcsin\left(2.6457513w\right)+\frac{2.6457513}{2\sqrt{7}}w\sqrt{1-7w^2}+C_0$
