Question

Selesaikan Integral berikut
1. X³dx/akar x²+1
2.integral 2sinx cosx dx
3.integral (x+2)³
mohon bantuaanya buat belajar buat materi ulangan + caranya

Answer 1

Maaf sekali saya tidak mengerti

Answer 2

1) int x³/√(x² + 1)  dx
= int x(x²)/√(x²+1)  dx
misal u = x² + 1 -------> x² = u - 1
du = 2x dx
1/2  du = x dx
maka integral di atas menjadi :
= int 1/2 (u - 1)/√u  du
= 1/2 int u^(1/2) - u^(-1/2)  du
= 1/2  (2/3 u^(3/2) - 2u^(1/2)) + C
= 1/3 u^(3/2) - u^(1/2) + C
= 1/3 u√u - √u + C
= 1/3 (x² + 1)√(x²+1) - √(x²+1) + C

2) int 2sin(x)cos(x) dx
= int sin(2x)  dx
= -1/2 cos(2x) + C

3) int (x+2)³ dx
= int (x³ + 6x² + 12x + 8) dx
= 1/4 x^4 + 2x³ + 6x² + 8x + C