calculo. hoja 6. integrales inmediatas. -...
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Dpto. Matematica Aplicada. E.T.S. Arquitectura. U.P.M. [email protected]
CALCULO.Hoja 6. Integrales inmediatas.
1.∫adx = ax+ C
2.∫xndx = xn+1
n+1+ C
3.∫
1xdx = log |x|+ C
4.∫
1√xdx = 2
√x+ C
5.∫exdx = ex + C
6.∫pxdx = px
log p+ C
7.∫sinxdx = − cosx+ C
8.∫cosxdx = sin x+ C
9.∫tanxdx = − log | cos x|+ C
10.∫sec x · tanxdx = sec x+ C
11.∫sec2 xdx = tanx+ C
12.∫cosec2 xdx = −cotanx+ C
13.∫
11+x2dx =
{arctanx+ C−arcotanx+ C
14.∫
1√1−x2dx =
{arcsin x+ C− arccosx+ C
15.∫f(x)n · f ′(x)dx = f(x)n+1
n+1+ C
16.∫ f ′(x)
f(x)dx = log |f(x)|+ C
17.∫ f ′(x)√
f(x)dx = 2
√f(x) + C
18.∫ef(x) · f ′(x)dx = ef(x) + C
19.∫f ′(x) · sin f(x)dx = − cos f(x) + C
20.∫f ′(x) · cos f(x)dx = sin f(x) + C
21.∫f ′(x) · tan f(x)dx = − log | cos f(x)|+ C
22.∫ f ′(x)
1+f(x)2dx =
{arctan f(x) + C−arcotan f(x) + C
23.∫ f ′(x)√
1−f(x)2dx =
{arcsin f(x) + C− arccos f(x) + C