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Using "Integration by parts" or "reverse chain rule" . Recall formula for intergration by parts: "∫f'(x) g(x) dx = f(x)g(x) - ∫f(x)g'(x)dx" Then set f'(x) = 1, g(x) = log(x). Ca...

Use the chain rule: f'(x) = v(du/dx) +u(dv/dx). Let u = 2x, du/dx = 2, v = lnx, dv/dx = 1/x Using this information: f'(x) = 2lnx + 2x/x This simplifies to f'(x) = 2lnx +2.

For each term the aim is to raise the power of x by 1 and divide by the new power. For this question, each part of the expression can be looked at seperately to make things a bit easier: ∫(1 + 3√x + 5x)dx = ...

This question may start by giving you an equation, which you need to write in the form of the standard equation of a circle (usually by completing the square). This allows you to see the centre of the circle...

A: x 3 /3 + 3ln(x) + A. Step-by-step solution: Integral (x 2 +3/x dx) = [as integrals preserve sums] integral (x 2 dx) + integral (3/x dx) = [raise exponent by one, multiply by the reciprocal, add a constant...