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Step 1 differentiate substitution: du/dx = -2sin(2x)Step 2 rearrange for dx: dx=du/-2sin(2x)Step 3 substitute: integral= ∫u²sin³(2x).du/-2sin(2x)Step 4 get the integral in terms of u...

 y=x(x−1)y= x^2-xdy/dx= 2x-1

By putting u=cosx and v’= e^x , use the by parts formula to get:∫e^(x)(cos(x)) dx = cos(x)e^x - ∫-(e^x)sin(x) dx. Use by parts again on the second term to get ∫ =cos(x)e^x + sin(x)e^x - ∫e^(x)(c...

Check to see if anything can be removed from withing the integral and taken out the front. In this case, 7/4 can be taken out the front (as it is not dependent on x), leaving only the term e^(x/2) to be i...

Firstly, to begin this problem we must think of the best way to substitute the given values into the formula. For a start, we are given the tangent at x=2. In other words, this is equal to the derivative ...