nilai dari integran 4-0 2x + 2/√x^2 + 2x + 1

jawab


₀⁴∫ (2x + 2) / √ (x²+2x +1) dx

u = x² + 2x + 1 
du = (2x + 2) dx

x= 0 --> u = 1
x= 4 --> u = 4²+2(4)+ 1  = 25

₀⁴∫ (2x+2) dx/ √(x²+2x + 1) = ₁ ²⁵∫ 1/√u du

= ₁²⁵∫ u^(-1/2) du

=  2 √ u ]²⁵₁

= 2(√25 - √1)

= 2 (5 -1)

= 8