You are Here: Home >< Maths

# Core 3 integration by substitution question Watch

1. Integrate sinxcosx (1+cosx)^4 dx

let U= 1+cosx

I got the answer as 1/5 (1+cosx)^5 - 1/6 (1+cosx)^6 + C

Is this correct?
2. (Original post by MSI_10)
Integrate sinxcosx (1+cosx)^4 dx

let U= 1+cosx

I got the answer as 1/5 (1+cosx)^5 - 1/6 (1+cosx)^6 + C

Is this correct?
It's the same as what I get. . .
3. yes
4. Yay
5. (Original post by MSI_10)
Yay
You can always do a quick check by differentiating the result you obtained:

d/dx [1/5 (1+cosx)^5 - 1/6 (1+cosx)^6 + C ]

= (-sinx)*(1+cosx)^4 - (-sinx)*(1+cosx )^5

= (-sinx)*(1+cosx)^4 + (sinx)*(1+cosx )^5

= (sinx)*(1+cosx)^4 [ -1+(1+cos x)]

= (sinx)*(1+cosx)^4 *(cos x)

= sinxcosx (1+cosx)^4 (shown)

So perfecto my friend, an integration problem well solved. Peace.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: March 28, 2013
Today on TSR

What should I do?

### How to go from a 4 to a 9 in GCSE Maths?

Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE