Trigonometric Subsitution Integral

[Painguy]

Homework Statement

∫cot^2(x)csc^4(x)dx

Homework Equations

The Attempt at a Solution

∫cot^2(x)(cot^2(x)+1)csc^2(x)dx
u=cot(x)
du=-csc^2(x)dx
-∫u^2 (u^2 +1)du
-∫u^4 + 2u^3 + u^2 du
-(u^5)/5 - (u^4)/2 - (u^3)/3
-cot^5(x)/5 - cot^4(x)/2 - cot^3(x)/3 + C

Wolfram alpha shows the solution as -cot^5(x)/5 - cot^3(x)/3 + C

So I'm unsure as to how I got the cot^4(x)/2

What exactly did I do wrong or is wolfram wrong?

Thanks in advance

 

[Dick]

Homework Statement

∫cot^2(x)csc^4(x)dx

Homework Equations

The Attempt at a Solution

∫cot^2(x)(cot^2(x)+1)csc^2(x)dx
u=cot(x)
du=-csc^2(x)dx
-∫u^2 (u^2 +1)du
-∫u^4 + 2u^3 + u^2 du
-(u^5)/5 - (u^4)/2 - (u^3)/3
-cot^5(x)/5 - cot^4(x)/2 - cot^3(x)/3 + C

Wolfram alpha shows the solution as -cot^5(x)/5 - cot^3(x)/3 + C

So I'm unsure as to how I got the cot^4(x)/2

What exactly did I do wrong or is wolfram wrong?

Thanks in advance

Now how did you change u^2(u^2+1) into u^4 + 2u^3 + u^2?