Integration

Can I use reverse chain rule to integrate an expression like x(2x+5)^1/2?

Study Forum Helper

Original post by Reisei

Can I use reverse chain rule to integrate an expression like x(2x+5)^1/2?

No. You can use it to integrate

(2x+5)^{1/2}

though

OP

Ok thank you, is there a rule for which expressions you can integrate using reverse chain rule?

assassinbunny123

Original post by Reisei

Ok thank you, is there a rule for which expressions you can integrate using reverse chain rule?

any expression with a power

Study Forum Helper

Original post by assassinbunny123

any expression with a power

Er... so we discarding

\sin(2x+1)

now?

Original post by Reisei

Ok thank you, is there a rule for which expressions you can integrate using reverse chain rule?

'Reverse chain rule' is essentially substitution. You can use it whenever you're integrating an expression of the form

g'(x) \cdot fg(x)

. where

fg(x)

means

f(g(x))

so that

g

is inside

f

.

I.e.

2x\sin(x^2+5)

or

(3x^2-2x+1)e^{x^3-x^2+x}

But I think the term itself is often used at A-Level when

g(x)

is a linear function so that

g'(x)

is a constant so it doesn't really matter.

These ones are simpler and have the form

(ax+b)^{\alpha}

(edited 5 years ago)

Original post by assassinbunny123

any expression with a power

if you're talking about such as

e^{2x}

then yes.

With the example you gave earlier, what you'll need is integration by parts.

Remember that during reverse chain rule, if you end up multiplying the expression with something that has the variable in it (x, or the one you're using), then you're using the wrong method.

(edited 5 years ago)

Study Forum Helper

Original post by DunkenDonuts

what you'll need is product rule.

For integration...?

Just complexify the integral ;-)

Original post by RDKGames

For integration...?

Oops, not differentiation. Sorry.

I'll edit the post. :smile:

:smile:

Original post by RDKGames

For integration...?

reverse product rule, ie integrating by parts

Quick Reply

Latest

Trending

Trending

Articles for you

Students react after A-level Maths Paper 3 on 20 June

Students react after A-level Maths Paper 3 on 20 June

What is an LLM and how could it benefit your career?

What is an LLM and how could it benefit your career?

Powerful questions business students forget to ask their career advisers

Powerful questions business students forget to ask their career advisers

Why I chose a law degree and what studying law was like

Why I chose a law degree and what studying law was like