# Some integral problems and some others

• Apr 28th 2009, 07:37 PM
KaTaNa111
Some integral problems and some others
1) the definite integral from 0-1 of e^sqrtx\sqrtx

2) indefinite integral of x+2/(sqrt(4-x^2)) (4-x^2 is all under the square root sign)

3) i wont use the ^ to denote exponents on this one to avoid confusion, but all numbers are exponents

indefinite integral of cos3x-sin2/cos2x

4) find the slope and the tangent line to the curve y=ln(xe^x) at the point x=3

5) solve for x: 2^3x-1=5

these are the 5 problems i need to do correctly and turn in tommarow to be done with my class, if anyone can post them up real quick step by step i would appreciate it
• Apr 28th 2009, 07:48 PM
Chris L T521
Quote:

Originally Posted by KaTaNa111
1) the definite integral from 0-1 of e^sqrtx\sqrtx

2) indefinite integral of x+2/(sqrt(4-x^2)) (4-x^2 is all under the square root sign)

3) i wont use the ^ to denote exponents on this one to avoid confusion, but all numbers are exponents

indefinite integral of cos3x-sin2/cos2x

4) find the slope and the tangent line to the curve y=ln(xe^x) at the point x=3

5) solve for x: 2^3x-1=5

these are the 5 problems i need to do correctly and turn in tommarow to be done with my class, if anyone can post them up real quick step by step i would appreciate it

It is against MHF policy to give full solutions (or even possibly hints) on material that counts towards someone's final grade . If you show us some effort on your part, we may give you hints on how to tackle the problems (if you get stuck). After all, this needs to be your own work, not our work.
• Apr 28th 2009, 07:50 PM
mr fantastic
Quote:

Originally Posted by KaTaNa111
1) the definite integral from 0-1 of e^sqrtx\sqrtx

2) indefinite integral of x+2/(sqrt(4-x^2)) (4-x^2 is all under the square root sign)

3) i wont use the ^ to denote exponents on this one to avoid confusion, but all numbers are exponents

indefinite integral of cos3x-sin2/cos2x

4) find the slope and the tangent line to the curve y=ln(xe^x) at the point x=3

5) solve for x: 2^3x-1=5

these are the 5 problems i need to do correctly and turn in tommarow to be done with my class, if anyone can post them up real quick step by step i would appreciate it

Please don't post so many questions in the one post. Otherwise the thread becomes long and confusing.
1) make the substitution $\displaystyle u = \sqrt{x}$.

2) $\displaystyle \int \! \frac{x + 2}{\sqrt{4 - x^2}} \, dx = \int \! \frac{x}{\sqrt{4 - x^2}} \, dx + \int \! \frac{2}{\sqrt{4 - x^2}} \, dx$

For the first, make the substitution $\displaystyle u = 4 - x^2$. The second is a standard form that you should know or look up.

3) cos3x-sin2/cos2x contains a typo. Please re-post the correct exprssion.

4) m = dy/dx. Note that $\displaystyle y = \ln (x e^x) = \ln (x) + \ln (e^x) = \ln (x) + x$ and each term is easily differentiated.

When $\displaystyle x = 3, ~ y = \ln (3) + 3$. You have a point and a gradient so it should be straightforward to get the equation of the line.

5) 2^3x-1=5 is ambiguous. Is it 2^(3x)-1=5 or 2^(3x-1)=5. Please re-post more clearly.

Edit: Please note what is said in post #2. If you need more help you will need to show some significant effort.