# A level Maths IntegrationWatch

#1
Hi TSR,

I am stuck on this integration question and how to answer it because I have reached a dead end.

y = sin(lnx)

I have integrated it by substitution to get:

pi/2
e^u sin(u)du
0

I then integrated it by parts to get

pi/2
[e^u sin(u)] - e^u cos(u)du
0

I am stuck because I don't know what to do next. If I integrate it again, I will end up repeating myself. Can someone direct me into what I need to do next, please?

Thanks!!!
0
6 months ago
#2
(Original post by Yodalam)
Hi TSR,

I am stuck on this integration question and how to answer it because I have reached a dead end.

y = sin(lnx)

I have integrated it by substitution to get:

pi/2
e^u sin(u)du
0

I then integrated it by parts to get

pi/2
[e^u sin(u)] - e^u cos(u)du
0

I am stuck because I don't know what to do next. If I integrate it again, I will end up repeating myself. Can someone direct me into what I need to do next, please?

Thanks!!!
When using integration by parts you sometimes need to do it twice.

If we represent your integral by I, then you end up with the situation

I = something - I

Hence 2I = something,

and I = something / 2
6 months ago
#3
Use the website 'integral calculator' - it shows steps if you unsure
1
#4
Hi,

I have integrated it again and now I have 2 integrals:

e^pi/2
I = [e^u sin(u)] - e^u cos(u)
1

e^pi/2
I = [e^u cos(u)] + e^u sin(u)
1

I don't know what steps to take now? Any help?

Thanks.
0
6 months ago
#5
For:

try integration by parts using:

(As "ghostwalker" states, you may need to apply integration by parts twice).
1
X

new posts
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

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

### University open days

• Solent University
Mon, 25 Mar '19
• Cardiff University
Wed, 27 Mar '19
• University of Portsmouth
Wed, 27 Mar '19

### Poll

Join the discussion

#### Where do you need more help?

Which Uni should I go to? (129)
17.97%
How successful will I become if I take my planned subjects? (73)
10.17%
How happy will I be if I take this career? (123)
17.13%
How do I achieve my dream Uni placement? (104)
14.48%
What should I study to achieve my dream career? (70)
9.75%
How can I be the best version of myself? (219)
30.5%