# Integral problem :(

• Oct 18th 2010, 11:27 AM
kunkka
Integral problem :(
Could someone solve this for me please?
I haven't got an idea how to solve this, therefore
Thank you.

a) 2e^(7x)/e^(5x) dx

b)x^2 sqrt (7-3x^3) dx

c) x^3 sqrt ( x-3) dx

Thank you! I don't need an explanation, I'll try to find out by my self,
Thanks
• Oct 18th 2010, 11:36 AM
e^(i*pi)
Quote:

Originally Posted by kunkka
Could someone solve this for me please?
I haven't got an idea how to solve this, therefore
Thank you.

a) 2e^(7x)/e^(5x) dx

b)x^2 sqrt (7-3x^3) dx

c) x^3 sqrt ( x-3) dx

Thank you! I don't need an explanation, I'll try to find out by my self,
Thanks

It's against the forum rules to completely give you the answer and working unless you've shown your working

a) $2\dfrac{e^{7x}}{e^{5x}} = 2e^{7x-5x} = 2e^{2x}$

Use the rule: $\int e^{ax} = \dfrac{1}{a}e^{ax}$

b) This requires you to use integration by parts twice

Integration by parts: $\int u\,dv = uv - \int v\,du$

Let $u = x^2$ to get you started.

c) As above but use it three times

If you do not understand show how far you get
• Oct 18th 2010, 12:12 PM
tom@ballooncalculus
Just in case a picture helps for b)...

http://www.ballooncalculus.org/draw/intChain/four.png

... where (key in spoiler) ...

Spoiler:
http://www.ballooncalculus.org/asy/chain.png

... is the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to the main variable (in this case x), and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).

The general drift is...

http://www.ballooncalculus.org/asy/maps/chain.png

Similarly, for c), using u = sqrt(x-3), i.e. x = u^2 + 3...

http://www.ballooncalculus.org/draw/intChain/five.png

Fill the blanks and continue the anti-clockwise journey towards the integral, I.

_________________________________________

Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

Balloon Calculus Drawing with LaTeX and Asymptote!
• Oct 18th 2010, 01:23 PM
kunkka
• Oct 18th 2010, 03:03 PM
mr fantastic
Quote:

Originally Posted by kunkka
[snip]

b)x^2 sqrt (7-3x^3) dx

c) x^3 sqrt ( x-3) dx

Thank you! I don't need an explanation, I'll try to find out by my self,
c) Substitute u = x - 3. Then expand $(u+3)^3 u^{1/2}$ and integrate term-by-term.