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A2 maths Integration via subsitution and expotenials questions

I have two questions which I cant do

1) use u=3-x^3 and integrate between 1 and 0 (x^5)/(3-x^3) dx ive put it in brackets to help I did du/du and then made it equal dx however I think logs come into it but couldn't do this question

2)3e^y +5e^-y =16 I thought of taking the 16 to the other side then factorising but didn't seem to work.

Thanks in advance !!!
Original post by joeheat
I have two questions which I cant do

1) use u=3-x^3 and integrate between 1 and 0 (x^5)/(3-x^3) dx ive put it in brackets to help I did du/du and then made it equal dx however I think logs come into it but couldn't do this question

2)3e^y +5e^-y =16 I thought of taking the 16 to the other side then factorising but didn't seem to work.

Thanks in advance !!!


For number 2

Multiply through by e^y and then try factorising it all
What have you done so far with number one? Have you sorted out how the substitution will take care of x^5? Show your work so far and I'll try to bump you along in the right direction with the logs.
Reply 3
Avatar for Hasufel
Hasufel
16
this is an interesting question. Notice, you cando it by using partial fractions.****

(hint: divide x^5 by x^3-3, then negate it, then multiply the remainder by -1, and the divisor by -1, so that you get the 1st line in latex below)

If you do so, the integrand splits as:

−x2+3x23−x3 \displaystyle -x^{2}+\frac{3x^{2}}{3-x^{3}}

(try it) - THEN substitute! - it`s not messy at all if you do this.

which makes integration WAY easier with the substitution you need to do.

***this is because you need to divide out, as degree numerator > degree denominator
(edited 9 years ago)
Reply 4
Avatar for davros
davros
16
Original post by Hasufel
this is an interesting question. Notice, you cando it by using partial fractions.****

(hint: divide x^5 by x^3-3, then negate it, then multiply the remainder by -1, and the divisor by -1, so that you get the 1st line in latex below)

If you do so, the integrand splits as:

−x2+3x23−x3 \displaystyle -x^{2}+\frac{3x^{2}}{3-x^{3}}

(try it) - THEN substitute! - it`s not messy at all if you do this.

which makes integration WAY easier with the substitution you need to do.

***this is because you need to divide out, as degree numerator > degree denominator


It actually works out quite nicely just using the substitution directly, providing you write x^5 as x^2 times x^3 :smile:
Reply 5
Avatar for Hasufel
Hasufel
16
Original post by davros
It actually works out quite nicely just using the substitution directly, providing you write x^5 as x^2 times x^3 :smile:


Doh! :wink:

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