I need solution step by step for these integrals

I have Maple but don't have options show me step by step

Could you help

Thanks

1. int(3*t/(4*t^2+4*t-11)^1/2,t)

2. int((x^3-x^2+x+1)/(x^2+1)*(x-1)^2,x);

3. int(exp(((x)^1/2)),x);

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- Aug 13th 2006, 05:45 AMsimfonijaIntegration please help
I need solution step by step for these integrals

I have Maple but don't have options show me step by step

Could you help

Thanks

1. int(3*t/(4*t^2+4*t-11)^1/2,t)

2. int((x^3-x^2+x+1)/(x^2+1)*(x-1)^2,x);

3. int(exp(((x)^1/2)),x); - Aug 13th 2006, 06:08 AMgalactus
Here's a link to the first one. Was that you?.

http://math2.org/mmb/thread/36961

#2 use partial fractions:

For #3, try the subsitution

- Aug 13th 2006, 12:15 PMSoroban
Hello, simfonija!

Here's my approach to #1 . . .

Quote:

Complete the square: .

So we have: .

Let

and the radical is: .

. . .

Substitute: .

. .

Back-substitute: .

We have: .

. .

- Aug 13th 2006, 01:05 PMThePerfectHackerQuote:

Originally Posted by**simfonija**

Express as,

Let, then,

Thus, you have,

Becomes,

Ignore the 2 and use integration by parts,

then,

then,

Thus, by parts,

Thus,

Multiply by two,

Substitute,

- Aug 13th 2006, 03:23 PMSoroban
Hello, simfonija!

Galactus had the best idea for #3 . . .

Quote:

Let

Substitute: .

Integrate by parts:

. . Let: .

. . Then:

And we have: .

Back-substitute: .

- Aug 13th 2006, 03:28 PMsimfonija
Thank you so much to all, can somebody help with the last one, I get lost in coificients, cant find A,B... I have just 15 min to submit my assignment

Thanks - Aug 13th 2006, 04:24 PMgalactus
#2:

Do the partial fraction thing:

This leads to the following system:

The solutions are

Break it into 2 integrals after you do the partial fractions.

For the first half:

For the 2nd half:

So, put 'er all together:

- Aug 13th 2006, 04:41 PMsimfonijasimfonija
Thanks again, great help.