tunde
∫e^x sin x dx = rumus int parsial = uv - ∫vdu
ambil u = sin x dan dv = e^x dx sehingga du = cos x dx v = e^x
∫e^x sin x = sinx e^x - ∫e^x cosx dx = e^x sin x - ∫e^x cosx dx misalkan : u = cos x dan dv = e^x dx sehingga du = -sin x dx v = e^x
∫e^x sin x dx = e^x sin x - ∫e^x cosx dx = [e^x sin x] - [ e^x cos x - ∫ e^x -sin x dx = e^x sin x - e^x cos x - ∫ e^x sin x dx ∫(e^x sin x + ∫ e^x sin x) dx = e^x (sin x - cos x) 2∫e^x sin x dx = e^x (sin x - cos x) ∫e^x sin x dx = 1/2{e^x (sin x - cos x)} + C
rumus int parsial = uv - ∫vdu
ambil u = sin x dan dv = e^x dx
sehingga
du = cos x dx
v = e^x
∫e^x sin x = sinx e^x - ∫e^x cosx dx
= e^x sin x - ∫e^x cosx dx
misalkan :
u = cos x dan dv = e^x dx
sehingga
du = -sin x dx
v = e^x
∫e^x sin x dx = e^x sin x - ∫e^x cosx dx
= [e^x sin x] - [ e^x cos x - ∫ e^x -sin x dx
= e^x sin x - e^x cos x - ∫ e^x sin x dx
∫(e^x sin x + ∫ e^x sin x) dx = e^x (sin x - cos x)
2∫e^x sin x dx = e^x (sin x - cos x)
∫e^x sin x dx = 1/2{e^x (sin x - cos x)} + C