Apéndice: Lista De Integrales - LEXIBOOK SC700_01 Manual Del Propietário

12. APÉNDICE: LISTA DE INTEGRALES
∫x dx = x /(n+1)
n n+1
dx/x = ln |x|
∫a dx = a /ln a
x x
∫(ax+b) dx = (ax+b)
n
∫(ax+b) dx = (1/a) ln |ax+b|
–1
∫e dx = (1/a)e
ax ax
∫baxdx = (1/a)b /ln b
ax
∫xe dx = (e /a2) (ax–1)
ax ax
∫ln axdx = xlnax – x
∫x ln ax dx = x /(n+1) ln ax–x
n n+1
∫x ln ax dx = (1/2) (ln ax
–1
∫dx/(x ln ax) = ln |ln ax|
∫cos ax dx = (1/a) sin ax
∫sin ax dx = –(1/a) cos ax
∫sin ax dx = (x/2)–(sin 2ax)/4a

∫cos ax dx = (x/2)+(sin 2ax)/4a

∫sinax cos bx dx=
–(cos(a+b)x/(2(a+b))+cos(a–b)x/(2(a–b))) cuando a
∫sin ax sin bx dx = sin(a–b)x/(2(a–b))–sin(a+b)x/(2(a+b))
cuando a ≠b
 
∫cos ax cos bx dx = sin(a–b)x/(2(a–b))+sin(a+b)x/(2(a+b))
avec a ≠b
 
∫sin ax cos ax dx = –(cos 2ax)/4a
∫(cos ax / sin ax) dx = (1/a) ln |sin ax|
∫(sin ax / cos ax) dx = –(1/a) ln |cos ax|
∫xsin ax dx = sin ax/a
∫xcos ax dx = (cos ax)/x
∫sinh ax dx = (cosh ax)/a
∫cosh ax dx = (sinh ax)/a
∫sinh ax dx = (cosh 2ax)/4a–x/2

∫cosh ax dx = (sinh 2ax)/4a+x/2

∫xsinh ax dx = x(cosh ax)/a–(sinh ax)/a
∫xcosh ax dx = x(sinh ax)/a–(cosh ax)/a
∫tanh ax dx = (ln cosh ax)/a
∫coth ax dx = (ln |sinh ax|)/a
∫tanh ax dx = x–(tanh ax)/a

∫coth ax dx = x–(coth ax)/a

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. 1/a(n+1) cuando n≠–1
n
/(n+1)
n+1
)

– (xcos ax)/a

+ (xsin ax)/a

cuando n≠–1

≠b
 


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