In order to use u-substitution, we have to think about what would be an appropriate u. As the denominator of the integrand has a form of something over square root of something minus something (that contains x) squared, the integrand has a form of the derivative for inverse sin. In order to use this derivative, I will modify the integrand.
*Note: Please ignore the grey area right next to the integration sign.
I think one way of recognizing how to modify and what value to use for "u" is to look for the general format of the integrand. For this question, as the integrand has a general form of A / (sqrt(B - CX^2)), you would expect the answer to this integrand would be somehow related to inverse sin. However, in order to integrate something to get to inverse sin, as the number inside the square root should be one, I modified the integrand so that the number inside the square root is one.
If you do enough practice on substitution questions, you would be able to quickly recognize and find appropriate "u" to use.
Hi,
Thank you for your question.
In order to use u-substitution, we have to think about what would be an appropriate u. As the denominator of the integrand has a form of something over square root of something minus something (that contains x) squared, the integrand has a form of the derivative for inverse sin. In order to use this derivative, I will modify the integrand.
*Note: Please ignore the grey area right next to the integration sign.
Hence, the answer would be the following:
Does this answer your question?