1. Ok, i have decided not to post many integral question like i did before but my keen interest in calculus makes me approach these questions almost everyday and i happen to stumble upon hard questions(at least for me), but i must say this integral isnt at all "tedious", its rather interesting i think, so i would appreciate any hints, (not answers) would be great. Thank you

i do sense some sort of generalization(obviously) for any powers of "x". Can anyone help me out??

2.

3. Im not trying to get this out free handily, rather i have approached myself but do not get the right answer.

4. Originally Posted by Heinsbergrelatz
Ok, i have decided not to post many integral question like i did before but my keen interest in calculus makes me approach these questions almost everyday and i happen to stumble upon hard questions(at least for me), but i must say this integral isnt at all "tedious", its rather interesting i think, so i would appreciate any hints, (not answers) would be great. Thank you

i do sense some sort of generalization(obviously) for any powers of "x". Can anyone help me out??
Try induction on n and integration by parts.

5. Originally Posted by Heinsbergrelatz
Ok, i have decided not to post many integral question like i did before but my keen interest in calculus makes me approach these questions almost everyday and i happen to stumble upon hard questions(at least for me), but i must say this integral isnt at all "tedious", its rather interesting i think, so i would appreciate any hints, (not answers) would be great. Thank you

i do sense some sort of generalization(obviously) for any powers of "x". Can anyone help me out??
Use integration by parts than apply a reduction formula.

6. Very simple.
Simply integrating by using integration by parts.

7. Very simple.
Simply integrating by using integration by parts.
If im not asking too much, why dont you show me how you would try this? I have actually solved it today,but actually for this question the answer isnt in the book, so i might never be sure if im right.

8. Originally Posted by Heinsbergrelatz
Very simple.
Simply integrating by using integration by parts.
If im not asking too much, why dont you show me how you would try this? I have actually solved it today,but actually for this question the answer isnt in the book, so i might never be sure if im right.
You have had several, duplicative, suggestions. Now work it out for yuorself. Yoou should, by now, be able to check and verify your work. Real problems do not come with answers "in the back of the book."

9. Originally Posted by Heinsbergrelatz
If im not asking too much, why dont you show me how you would try this? I have actually solved it today,but actually for this question the answer isnt in the book, so i might never be sure if im right.
Use the fundamental theorem of calculus to check your solution.

10. The thing is I get a factorial in my answer, and that seems weird. I ususally dont get in most of my integral questions

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