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y = arctan(x)tan(y) = xsec 2 (y) = dx/dyfrom cos 2 A + sin 2 A = 1, we know that 1 + tan 2 A = sec 2 A (divide by cos 2 A), so we substitute in1 + tan 2 (y) = dx/dyfrom the initial relationship,1 + x 2 = dx/...

This indefinite integral (has no defined limits) should be evaluated by integration by substitution This is because you cannot integrate sin 2 xWhen doing integration by substitution, the first thing we need...

This can be done with integration by substitution. If we let u=tanx then du/dx=sec^2(X). If we substitute U into the integrand we get it being u(sec^2(X))dx. rearranging the du/dx equation to make dx the sub...

To start with, we want to put this into quadratic form, where we have ax^2+bx+c=0. We notice that there are terms on both sides of the equation. So we can expand the right hand side and then bring all the te...

Firstly, we need the equation to be in terms of one cosh argument if possible, which can be done by the identity cosh 2x = 2cosh 2 x - 1. Upon substitution and simplification we get 6cosh 2 x - 29cosh x + 35...