integration formulas

INTEGRATION FORMULAS This page contains a list of commonly used integration formulas. 1. 1 1 r r x x dx C r + = + + ∫ 2. ( ) ( ) kf x dx k f x dx = ∫ ∫ (where is a constant) k 3. ( ) ( ) ( ) ( ) f x gx dx f x dx gx dx ± = ± ⎡ ⎤ ⎣ ⎦ ∫ ∫ ∫ 4. Integration by Substitution ( ) ( ) f u du Fu C = + ∫ where and ( ) u gx = ( ) ' du g x dx = Also written as: ( ) ( ) ( ) ( ) ( ) ' f gx g x dx Fgx C = + ∫ 5. u u e du e C = + ∫ 6. ln u u a a du C a = + ∫ 7. 1 ln dx u C u = + ∫ 8. Integration by Parts u dv uv v du ⋅ = ⋅ − ⋅ ∫ ∫ 9. cos sin u du u C = + ∫ 10. sin cos u du u C =− + ∫ 11. 2 sec tan u du u C = + ∫ 12. 2 csc cot u du u C =− + ∫ 13. sec tan sec u u du u C = + ∫ 14. csc cot csc u u du u C =− + ∫ 15. tan ln sec u du u C = + ∫ 16. cot ln sin u du u C = + ∫ 17. sec ln sec tan u du u u C = + + ∫ 18. csc ln csc cot u du u u C = − + ∫ 19. 1 2 2 sin du u C a a u − ⎛ ⎞ = + ⎜ ⎟ ⎝ ⎠ − ∫ 20. 1 2 2 1 tan du u C a u a a − ⎛ ⎞ = + ⎜ ⎟ + ⎝ ⎠ ∫ 21. 1 2 2 1 sec du u C a a u u a − ⎛ ⎞ = + ⎜ ⎟ ⎝ ⎠ − ∫ 22. ln ln u du u u u C = − + ∫ 23. 2 1 1 sin sin 2 2 4 u du u u C = − + ∫ 24. 2 1 1 cos sin 2 2 4 u du u u C = + + ∫ 25. 2 tan tan u du u u C = − + ∫ 26. 2 cot cot u du u u C = − − + ∫ revised 12/07

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basic integration formulas

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INTEGRATION FORMULAS This page contains a list of commonly used integration formulas. 1.11rrxx dx Cr+= ++ 2. ( ) ( ) kf x dx k f x dx = (where is a constant)k 3. ( ) ( ) ( ) ( ) f x g x dx f x dx g x dx = 4.Integration by Substitution ( ) ( ) f u du Fu C = + where and ( ) u g x = ( ) ' du g x dx = Also written as: ( ) ( ) ( ) ( ) ( )' f g x g x dx F g x C = + 5.u uedu e C = +6.lnuuaadu Ca= + 7.1ln dx u Cu= + 8.Integration by Parts udv uv v du = 9. cos sin u du u C = + 10. sin cos u du u C = + 11.2sec tan u du u C = + 12.2csc cot u du u C = +13.sec tan sec u u du u C = + 14.csc cot csc u u du u C = + 15.tan lnsec u du u C = + 16.cot lnsin u du u C = + 17.sec lnsec tan u du u u C = + + 18.csc lncsc cot u du u u C = + 19. 12 2sindu uCaa u = + 20. 12 21tandu uCa u a a = + + 21. 12 21secdu uCa au u a = + 22.ln ln u du u u u C = + 23. 21 1sin sin22 4udu u u C = + 24. 21 1cos sin22 4udu u u C = + + 25. 2tan tan u du u u C = + 26. 2cot cot u du u u C = + revised 12/07

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