Integral

Bentuk Umum nya :

\int\,UdV = UV – \int\,Vdu

Contoh:

1). U=x —-> du = dx

dv = sin x —> v = -cos x

maka,

\int\,U dV = UV – \int\,Vdu

= x ( -cos x) – \int\,-cos x dx

= -x cos x + \int\,cos x dx

= -x cos x sin x + c

2). mis : U = sin x —> du = cos x dx

dv = x dx —> v =1/2 x²

maka:

\int\,U dV = UV –\int\,v du

= sin x½ x²) – \int\,½ x² cos x dx

= ½ x² sin x – ½ \int\,x ² cos x dx

3). \int\,ex ln X dx

mis : U = ln x —> du = dx/x

                 dv = ex dx = v= ex

\int\,UdV = UV- \int\,Vdu

= ln x . ex\int\,ex dx/x

= ex ln x – U = ex  —-> du = ex dx 

                                    dv = dx/x —> V = ln x

                                   UV – \int\,v du

                = ex ln x -( ex ln x – \int\,ln x  ex dx )

= –\int\, ln x  ex dx

= – soal

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