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Hint: Use the chain rule

Answer: dy/dx = 4e^(2x+1)

Integrate y=x^2 which is 1/3 x^3 Subsitute the limits, (1/3 (3)^3)-(1/3 (1)^3) 27/3 - 1/3 = 26/3

As why is in the for y=uv where u and v are funtions of x, dy/dx=u'v+v'u (where ' implies the derivative) u=(3x+1)², v=cos(3x) therefore using the chain rule u'=23(3x+1)=18x+6 and v'=-...

written out

Use integration by parts

let u=ln(x)

let dv/dx=x

therefore du/dx=1/x and v=(1/2)x^2

therefore the integral of xln(x) is equal to the following:

(1/2)x^2ln(x) - (integral...