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Integrals with Trigonometric Functions Z sinaxdx= 1 a cosax (63) Z sin2 axdx= x 2 sin2ax 4a (64) Z sinn axdx= 1 a cosax 2F 1 1 2; 1 n 2; 3 2;cos2 ax (65) Z sin3 axdx= 3cosax 4a + cos3ax 12a (66) Z cosaxdx=
Table of Basic Integrals Basic Forms (1) Z xndx= 1 n+ 1 xn+1; n6= 1 (2) Z 1 x dx= lnjxj (3) Z udv= uv Z vdu (4) Z 1 ax+ b dx= 1 a lnjax+ bj Integrals of Rational Functions (5) Z 1 (x+ a)2 dx= 1 x+ a (6) Z ... Integrals with Trigonometric Functions (71) Z sinaxdx= 1 a cosax (72) Z sin2 axdx= x 2 sin2ax 4a (73) Z sin3 axdx= 3cosax 4a + cos3ax 12a ...
Integrals of Exponential and Logarithmic Functions. ∫ ln x dx = x ln x − x + C. + 1 x. + 1. x ∫ x ln xdx = ln x − + C. 2 + 1 ( n + 1 ) x dx = e x + C ∫.
Table of Basic Integrals1 (1) Z xn dx = 1 n+1 xn+1; n 6= 1 (2) Z 1 x dx = lnjxj (3) Z u dv = uv Z vdu (4) Z e xdx = e (5) Z ax dx = 1 lna ax (6) Z lnxdx = xlnx x (7) Z sinxdx = cosx (8) Z cosxdx = sinx (9) Z ... CSUN, Integrals, Table of Integrals, Math 280, Math 351, Differential Equations Created Date:
Table of Integrals. 1. ur+1(x) [u(x)]ru0(x) dx = C, r 6=−1. r. 2. Z u0(x) dx. = ln |u(x)| u(x) 1. C. 3. eu(x)u0(x) dx = eu(x) + C. 4. Z. sin [u(x)] u0(x) dx = − cos u(x) + C. 5. cos [u(x)] u0(x) dx = sin u(x) + C. 6. tan [u(x)] u0(x) dx = ln | sec u(x)| + C. 7. Z. cot [u(x)] u0(x) dx = ln | sin u(x)| + C. 8. Z.
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Table of Integrals 1. Z ur du = ur+1 r +1 +C, r 6=−1 2. Z 1 u du =ln|u|+C 3. Z eu du = eu +C 4. Z sinudu= − cosu+C 5. Z cosudu= sinu+C 6. Z tanudu=ln|secu|+C 7. Z cotudu=ln|sinu|+C 8. Z secudu=ln|secu+tanu|+C 9. Z cscudu=ln|cscu−cotu|+C 10. Z secutanudu= secu+C 11. Z cscucotudu= − cscu+C 12. Z sec2 udu= tanu+C 13. Z csc2 udu= − cotu+C ...
