Tolong dong pakai cara terimakasih 1. ∫2x(x^2+4)^5 dx ( integral 2x (x pangkat 2 +4)pangkat 5 dx 2. Integral batas atas 4 batas bawah 3 x (2 + x) ^3 dx Tolong d

jawab

∫ 2x ( x² + 4)⁵ dx

u = x²+ 4
du = 2x dx

∫ 2x (x² + 4)⁵ dx = ∫ u⁵ du = 1/6 u⁶ + c
= 1/6 (x² +4)⁶ + c


2)

₃⁴∫  x (2 +x)³ dx

u = 2 + x ---> du = dx
atau
x = u - 2
x= 3 --> u= 5
x = 4 --> u = 6

₃⁴∫ x (2+x)³ dx =
=  ₅⁶∫ (u-2)(u³) du
= ₅⁶∫ u⁴ - 2u³ du
=   [ 1/5 u⁵ - 1/2 u⁴]⁶₅

= 1/5[6⁵-5⁵) - 1/2 (6⁴-5⁴)
= 930,2 - 335,5
= 594,7