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Integral_Table

# Integral_Table - ax C 19 R csc ax =-1 a log csc a x cot a x...

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September 9, 2010 1-1 A short table of integrals 1. A a constant = R Adx = Ax + C , 2. n 6 = 0 , 1 = R x n dx = x n +1 n +1 + C 3. R dx x = log ( x ) + C ; Integration by parts: R udv = uv - R vdu 4. R e ax dx = 1 a e ax + C ; Substitution: u = u ( x ) , R udu = R u ( x ) u 0 ( x ) dx 5. R xe ax dx = e ax ( x a - 1 a 2 ) + C 6. R x 2 e ax dx = e ax ( x 2 a - 2 x a 2 + 2 a 3 ) + C 7. R log ( ax ) = xlog ( ax ) - x + C 8. R xlog ( ax ) = x 2 2 log ( ax ) - x 2 4 + C 9. R dx a 2 + x 2 = 1 a arctan ( x a ) + C 10. R dx a 2 - x 2 = 1 2 a log ( x + a x - a ) + C 11. R dx a 2 - x 2 = arcsin ( x a ) + C 12. R dx x 2 - a 2 = log ( x + x 2 - a 2 ) + C 13. R dx a 2 + x 2 = arcsinh ( x a ) + C 14. R sin ( ax ) = - 1 a cos ( ax ) + C 15. R cos ( ax ) = 1 a sin ( ax ) + C 16. R tan ( ax ) = 1 a log ( sec ( ax )) + C 17. R cot ( ax ) = 1 a log ( sin ( ax )) + C 18. R sec ( ax ) = 1 a log ( tan ( ax ) + sec
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Unformatted text preview: ( ax )) + C 19. R csc ( ax ) =-1 a log ( csc ( a * x ) + cot ( a * x )) + C 20. R x cos ( ax ) = x sin ( ax ) a + cos ( ax ) a 2 + C 21. R e ax sin ( bx ) = e ax a 2 + b 2 ( a sin ( bx )-b cos ( bx )) + C 22. R e ax cos ( bx ) = e ax a 2 + b 2 ( b sin ( bx ) + a cos ( bx )) + C...
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