2. When applying the formula for integration by parts, how do ...

Question

2. When applying the formula for integration by parts, how do you choose the u and dv? How can you apply integration by parts to an integral of the form ∫ f(x) dx?

Accepted Answer

Welcome back everyone. When applying integration by parts to the integral x squared LN XDX, what should be the value for V according to the LIATE rule? So according to the LIATE mnemonic, which stands for logarithmic, inverse trigonometric, algebraic, trigonometric, and exponential. It dictates that the function type appearing earlier in the acronym should be chosen as u. So for the integral that we have, notice that there is an algebraic part which is x 2. We can call it capital A. And we also have ln of x, which is Lager redneck. So according to the rule, L goes first, which essentially means that we're going to set u equals L and x. Let's remember the integration by parts. The integration of UDV is equal to UV minus the integral of VDU. So now if u equals L of x, the remaining part dV is going to be equal to. X 2 multiplied by d x And this is how we can identify v. If dV is equal to x 2 dx, then v, which is the integral of dv, must be the integral of the right hand side of the equation. And as the integral of x 2 dx, we can find this integral by applying the power rule. So we get x to the power of 2 + 1, which is x cubed, divided by 3. We do not have to add a constant of integration. We can simply label this as our final answer for the. Thank you for watching.

2. When applying the formula for integration by parts, how do you choose the u and dv? How can you apply integration by parts to an integral of the form ∫ f(x) dx?

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