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This will use the process of integration by parts. First, notice that ln(x)=ln(x)*1. So, the integral of ln(x) is the integral of ln(x) 1. The process of integration by parts is; int (v du / dx ) dx =vu - in...

Sound waves have mass, as they are the longitudinal (along the path of the wave) vibration shockwave of molecule, while light waves do not, as they are the transverse displacement of just energy. Sound waves...

Take any polynomial, eg/ y=x 3 + 1 / 2 x 2 -3x+9. Then dy / dx =3x , +x-3, in this case. This is because, when deriving in this sense, you take each term in x, multiply it by its index, and reduce that index...

The claim that tolerance is important to liberals is not controversial. Voltaire famously declared that “I detest what you say, but will defend to the death your right to say it”. This reflects the idea that...

Take any quadratic equation, eg/ 3x 2 +4x-2=5 , and rearrange to equal 0 , ie/ 3x 2 +4x-7=0 (if you have an expression, ie/ there is no equals sign, then simply equate the expression to 0 ). Now, we use the ...