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The product rule, says that the derivative of a product is the sum gotten by differentiating each factor as if the other were constant and adding up the results. We can read this backwards as a way to handle an integrand of the form fg, when we know how to handle the integrand f g. For, we can write the product rule as fg = (fg) - f g and integrating both sides tells us This statement is called "integrating by parts" and is useful for integrands like xkexp(x) or ln(x) or xln(x). For example, to integrate ln(x), set f(x) = ln(x) and g(x)= 1. Then and g(x) = x. We can conclude that the integral of ln(x) from a to b is bln(b) - aln(a) - (b - a).

The product rule, says that the derivative of a product is the sum gotten by differentiating each factor as if the other were constant and adding up the results.

We can read this backwards as a way to handle an integrand of the form fg, when we know how to handle the integrand f g. For, we can write the product rule as

fg = (fg) - f g

and integrating both sides tells us

This statement is called "integrating by parts" and is useful for integrands like xkexp(x) or ln(x) or xln(x).

For example, to integrate ln(x), set f(x) = ln(x) and g(x)= 1. Then and g(x) = x.

We can conclude that the integral of ln(x) from a to b is bln(b) - aln(a) - (b - a).

Grade:12

1 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
8 years ago
Dear student,

The product rule is stated is for derivatives
And in integration we have a rule called integration by parts

both are different , you are mixing up things

Check definitions again !

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