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useful integration table

# useful integration table - 1 2 3 4 5 6 7 8 9 10 11 12 13 14...

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1. ∫∫ + = + dx x g dx x f dx x g x f ) ( ) ( )) ( ) ( ( 2. = dx x g dx x f dx x g x f ) ( ) ( )) ( ) ( 3. = ) ( ) ( ) ( ) ( ) ( ) ( x df x g x g x f x dg x f 4. C a a dx a x x + = ln , , 1 a 0 > a 5. C n x dx x n n + + = + 1 1 , 1 n 6. C x dx x + = ln 1 7. + = C e dx e x x 8. + = C x xdx cos sin 9. + = C x xdx sin cos 10. + = C x xdx tan sec 2 11. + = C x xdx cot csc 2 12. + = C x xdx x sec tan sec 13. + = C x xdx x csc cot csc 14. C n a b ax dx b ax n n + + + = + + ) 1 ( ) ( ) ( 1 , , 0 a 1 n 15. + + = + C b ax a dx b ax ln 1 ) ( 1 , 0 a 16. + + + + + = + + C n b n b ax a b ax dx b ax x n n 1 2 ) ( ) ( 2 1 , , 0 a 2 , 1 n 17. C b ax a b a x dx b ax x + + = + ln ) ( 2 1 , 0 a 18. C b ax b b ax a dx b ax x + + + + = + ln 1 ) ( 2 2 , 0 a 1 6

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19. + + = + C b ax x b b ax x dx ln 1 ) ( , 0 b 20. C n a b ax dx b ax n n + + + = + + ) 2 ( ) ( 2 ) ( 2 , , 0 a 2 n 21. + + + = + b ax x dx b b ax dx x b ax 2 22. + + = + C b b ax b b ax x dx 1 tan 2 , 0 < b 23. + + + + = + C b b ax b b ax b b ax x dx ln 1 , 0 > b 24. + + + + = + C b ax x dx a x b ax dx x b ax 2 2 25. ∫∫ + + + = + C b ax x dx b a bx b ax b ax x dx 2 2 , 0 b 26. C a x a x a dx + = + 1 2 2 tan 1 , 0 a 27. + + + = + C a x a x a a x x a dx 1 3 2 2 2 2 2 2 tan 2 1 ) ( 2 ) ( , 0 a 28. + + = C a x a x a x a dx ln 2 1 2 2 , 0 a 29. + = 2 2 2 2 2 2 2 2 2 2 1 ) ( 2 ) ( x a dx a x a a x x a dx , 0 a 30. + + + = + C x a x x a dx ) ln( 2 2 2 2 31. C x a x a x a x dx x a + + + + + = + ) ln( 2 2 2 2 2 2 2 2 2 32. C x a x a x a x a x dx x a x + + + + + = + ) ln( 8 ) 2 ( 8 2 2 4 2 2 2 2 2 2 2 33. C x x a a a x a dx x x a + + + + = + 2 2 2 2 2 2 ln 34. C x x a x a x dx x x a + + + + = + 2 2
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useful integration table - 1 2 3 4 5 6 7 8 9 10 11 12 13 14...

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