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Integrate by parts: integral = [uv] - ∫u'v dx (u'= derivative of u, v'= derivative of v)

u= x     u'= 1

v' = sin2x        v= -0.5cos2x

= -0.5xcosx  -  ∫-0.5cos2x dx

= -0.5xcosx...

Integrate, y= 3x² -1/x

 1{³ 3x² - 1/x dx = [x-lnx]³₁= (3-ln3)-(1-ln1) = 3-ln3-1+0= 2-ln3

First of all, let's start by defining the word 'interest'. Interest in mathematical terms generally means an amount of money that is accumulated over a period of time after an amount of money is invested ...

f(1)=0

f(x)=(x-1)(x+4)(x-2)

Equation: a+3 = (2a+7)/r

First, we want to rearrange the equation, so that the 'r', which is the denominator of the right hand side, multiplies with (a+3), creating r(a+3) = 2a+7. ...