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Further Mathematics
A Level

How do I integrate arctan(x) using integration by parts?

This is an example where we use integration by parts, but it is not immediately obvious where to start.Recall the integration by parts formula ∫u(dv/dx) dx = uv - ∫(du/dx)v dx
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Answered by Oliver C. Further Mathematics tutor
9326 Views

Integrate xsin(x).

The technique we need to use to solve this integral is called integration by parts. The parts formula is: the integral of (uv' dx) = uv - the integral of (u'v dx) (where u and v are functions of x). We ne...

Answered by Jakub W. Further Mathematics tutor
2051 Views

'Find the first derivative, with respect to x, of arctan(1/x) for non-zero real x. Hence show that the value of arctan(x)+arctan(1/x) is constant for all non-zero x, explicitly stating this constant in your final answer.' How do I solve this?

I have linked the solution to this problem here.

https://www.icloud.com/iclouddrive/0mLKDeFREhbvTJm6D09jFakcw#Solution

2010 Views

Solve this equation: x^2 + 2x + 2

x = (-2 +/- sqrt(4-8))/2                    therefore x = - 1 +/- i, where i is the imaginary unit

Answered by Alexander E. Further Mathematics tutor
1740 Views

Given that x = i is a solution of 2x^3 + 3x^2 = -2x + -3, find all the possible solutions

x = i is a solution, and all the coefficients are real, so x = -i must also be a solution:2x^3+3x^2+2x+3 = 0(x+i)(x-i)(Ax+B) = 0 (we argued above that this must be the case)(x^2+1)(Ax+B) = 0(x^2+1)(2x+3) ...

Answered by Ben S. Further Mathematics tutor
1658 Views

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