Question

Integration substitution:

Answer 1

integral of \[\frac{ -x^4 }{ \sqrt{x^5+2} } dx\]

Answer 2

Can someone explain step by step how this substitution works please? Thank you.

Answer 3

assume x^5+2 =z^2
so that 5x^4 dx = 2z dz and then proceed further

Answer 4

Let u = x^5 + 2

du/dx = 5x^4

du = 5x^4 . dx

1/5 du = x^4 . dx

Answer 5

How does this substitute BACK into the original equation? This is what I don't understand.

Answer 6

sincethere is a sqrt in the denominator it would be better to assume the denominator as some perfect squares

Answer 7

Any input Zak?

Answer 8

Oh NO! I clicked close accidently :(

Answer 9

assume x^5+2 =z^2 so that 5x^4 dx = 2z dz
so the required integration can be re written as integration of
-(1/5) *(5x^4) dx/(sqrt(x^5+2)
on substitution x^5+2 =z^2 and 5x^4 dx = 2z dz
we have the question as
(-1/5) 2zdz/sqrt(z^2)
thus we e now the integration of
(-2/5) dz
which on integration gives
(-2/5) z + c
now we have z= sqrt(x^5+2)
hence our answer is (-2sqrt(x^5+2)/5) + c

Answer 10

Thanks! :)

Answer 11

welcome dear
well i hope u have understood