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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 need ...
JW
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'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
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Solve this equation: x^2 + 2x + 2

x = (-2 +/- sqrt(4-8))/2 therefore x = - 1 +/- i, where i is the imaginary unit
AE
2622 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) = 0...
BS
2493 Views

Find the general solution to the differential equation y'' + 4y' + 3y = 6e^(2x) [where y' is dy/dx and y'' is d^2 y/ dx^2]

First find the general solution to the differential equation y'' + 4y' + 3y = 0 as an arbitrary number of the solution to this differential equation can be added to the solution of the differential equation ...
ES
6014 Views