Integration Help! (1 Viewer)

[overRun]

int[xsqrt(x+1)]dx
(i) using substitution u = x+1
(ii) using the substitution u^2 = x+1

int[x^5sqrt(1-x^3)]dx

int[x^2/(x-2)(x^2+2x+2)]dx

 

[Timothy.Siu]

umm u just substitute them in,

2nd one just use the substitution u=1-x^3 or u^2=1-x^3

3rd one just use partial fractions

 

[shaon0]

int[xsqrt(x+1)]dx
(i) using substitution u = x+1
(ii) using the substitution u^2 = x+1

int[x^5sqrt(1-x^3)]dx

int[x^2/(x-2)(x^2+2x+2)]dx

S x.sqrt(x+1) dx
1) Let u=x+1
S (u-1)sqrt(u) du
(2/5)(x+1)^(5/2)-(2/3)(x+1)^(3/2)+C

ii) Let u^2=x+1
u=sqrt(x+1), x>0
dx=2(u) du

S (u^2-1) 2u^2 du
= (2/5)(u)^(5)-(2/3)(u)^3+C
= (2/5)(x+1)^(5/2)-(2/3)(x+1)^(3/2)+C