## anonymous 4 years ago How do I integrate this?

1. anonymous

|dw:1326789204685:dw|

2. anonymous

Is this how to do it? |dw:1326789228310:dw|

3. anonymous

No, your last step is incorrect (try taking the derivative of your final expression to see why)

4. anonymous

Instead, you need to use the identity $\int \frac{dx}{x^2+a^2}=\tan^{-1}\frac{x}{a}+C$ Take the derivative of the right expression to see why this works!

5. anonymous

you'll need some trigonometry to make the u-substitution u = tan(x)/5

6. ash2326

no , $\int\limits_{}^{} 40/( x^{2}+25) dx$ $\int\limits_{}^{} 40/(x^2+5^2) dx$ $40 \tan^{-1} (x/5) +c$

7. anonymous

How can I work with that? |dw:1326789616311:dw|

8. anonymous

By the chain rule: $\frac{d}{dx}\tan^{-1}\frac{x}{a}=\frac{1}{1+(\frac{x}{a})^2} \cdot \frac{1}{a}$ Simplify a bit and you will get your answer.

9. anonymous

Sorry, the identity is $\int \frac{a \cdot dx}{x^2+a^2}=\tan^{-1}\frac{x}{a}+C$ My bad.

10. anonymous

Thus, for the sake of completeness, the answer is $\int \frac{40dx}{x^2+25}=8\tan^{-1}\frac{x}{5}+C$

11. anonymous

Do you multiply 40 by (1/5) because of the chain rule?

12. anonymous

Mhm, that you do!