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In order to integrate ln x you have to use integration by parts, even though it appears there is only one term to be integrated. We get around this by instead writing it as (ln x)(1), where we treat the 1...

A) 4(cosec²(2x)) - (cosec²(x)) = 4/(sin²(2x)) - 1/(sin²(x)) = 4/[(2 sin(x) cos(x))²] - 1/(sin²(x)) B) 4/[(2 sin(x) cos(x))²] - ...

As we are given the derivative of f(x), we first need to integrate this derivative to obtain the function, f(x). Using the standard integration formula, ∫ x^n dx = (1/n+1)(x^(n+1)) +c, integrate each term...

Here, we use integration by parts. We must imagine ln(x) as a product of 1 and ln(x). We usually take the function of x to be our dv/dx, however, in the case of ln(x), we take that to be u (it is a specia...

This problem uses the binomial expansion formula: (x+y)ⁿ= _k=0Zⁿ _nC_k x^k y^n-k.But lets try to understand where this formula comes...