INTEGRAL

Bentuk Umum nya :

UdV = UV – Vdu

Contoh:
1). U=x —-> du = dx
dv = sin x —> v = -cos x
maka,
U dV = UV – Vdu
= x ( -cos x) – -cos x dx
= -x cos x + 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:
U dV = UV -v du
= sin x½ x²) – ½ x² cos x dx
= ½ x² sin x – ½ x ² cos x dx
3). e^x ln X dx
mis : U = ln x —> du = dx/x

                 dv = e^x dx = v= e^x

UdV = UV- Vdu
= ln x . e^x- e^x dx/x
= e^x ln x – U = e^x  —-> du = e^x dx 

                                    dv = dx/x —> V = ln x

                                   UV – v du

                = e^x ln x -( e^x ln x – ln x  e^x dx )
= - ln x  e^x dx
= – soal