- #1

chwala

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- Homework Statement
- See attached.

- Relevant Equations
- Integration

For part (a),

Using partial fractions (repeated factor), i have...

##7e^x -8 = A(e^x-2)+B##

##A=7##

##-2A+B=-8, ⇒B=6##

$$\int {\frac{7e^x-8}{(e^x-2)^2}}dx=\int \left[{\frac{7}{e^x-2}}+{\frac{6}{(e^x-2)^2}}\right]dx$$

##u=e^x-2##

##du=e^x dx##

##dx=\dfrac{du}{e^x}##

...

also

##u=e^x-2##

##e^x=u+2##

$$\int {\frac{7e^x-8}{(e^x-2)^2}}dx=\int \left[{\frac{7}{e^x-2}}+{\frac{6}{(e^x-2)^2}}\right]=\int \left[{\frac{7u+6}{(e^x-2)^2}}\dfrac{du}{e^x}\right]=\int \left[{\frac{7u+6}{u^2(u+2)}}du\right]$$

...part b later...taking a break.

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