9–40. Integration by parts Evaluate the following integrals us...

Question

9–40. Integration by parts Evaluate the following integrals using integration by parts.

17. ∫ x · 3x dx

Accepted Answer

Evaluate the integral of 5 X multiplied by X the X using integration by parts. Now, to solve this by integration by parts, we first need to choose you. I've written a little chart here on the right that tells us how we can choose you. You will be first chosen with log, then inverse trach, then polynomial, then exponential, then triculometric functions. In this case, we have 5 risk the X. Which is an exponential And we have X, which is a polynomial function. We will then let U equals X. Which means DV equals 5 rates to the X. Now we can look at the formula for integration by parts. This is given by the integral. Of you DV equals UV minus the integral of VDU. We can then CDU will be one. And then we need to find the. V will just be the integral of 5 to the X. We do know the integral of AX is given by A X divided by natural log of A. We can then say V will be 5 X divided by natural log of 5. Now we can fill out our equation. We have the integral of 5 rates to the X X D X equals U, which is X. V, which is 5 to the X divided by natural log of 5. Minus the integral Of 5 to the X divided by natural log of 5. DU, which is just 1 DX. Now, from here, we can solve our second integral that's spots. We have X multiplied by 5 to the X, divided by natural log of 5. Minus 5 x divided by a natural log of 5. Squared Since we found the integral of 5 of the X before, we can repeat that, and we end up getting two natural log of 5s. Now we can go ahead and factor some terms out. We can factor out. By the X divided by natural log of 5 squared. And multiply this by X, natural log of 5. -1. Not because this is indefinite. We will add C at the ends. This is the final answer to our problem. OK, I hope to help you solve it. Thank you for watching. Goodbye.

9–40. Integration by parts Evaluate the following integrals using integration by parts.17. ∫ x · 3x dx

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9–40. Integration by parts Evaluate the following integrals using integration by parts.
17. ∫ x · 3x dx