Question

[text]\int\limits^1_0 { \frac{x+1}{( x^{2}+2x+2)^{2} } } \, dx

Tolong ya pake cara integral substitusi. Kalau bingung, cek fotonya [text]

Answer 1

U = x² + 2x + 2
du = 2x+ 2  dx
du = 2(x+1) dx
(x+1) dx = 1/2 du.
.
batas inetrgal
u = x² + 2x + 2
x = 1 --> u = 5
x = 0--> u = 2

₀¹∫ (x+1)/(x²+2x+2)² dx = ₂⁵∫(¹/₂ u⁻²) du
= - ¹/₂ [ 1/u]⁵₂ 
= - ¹/₂ { 1/5 - 1/2 }
= - ¹/₂ {⁻³/₁₀}
= ³/₂₀