## AmTran_Bus one year ago Integrate

1. AmTran_Bus

|dw:1433471626709:dw|

2. zepdrix

Oo that's a fun problem :)

3. zepdrix

So what are we having trouble with, power rule on that first term ya?

4. AmTran_Bus

I just have no clue what to do.

5. zepdrix

$\Large\rm \int\limits x^{\text{#}}dx=\frac{1}{\text{#+1}}x^{\text{#+1}}$The exponent is just a number. We just apply our power rule for integration to that first term. e is just a fancy number.

6. zepdrix

$\Large\rm \int\limits x^{3}dx=\frac{1}{4}x^{4}$$\Large\rm \int\limits x^e dx=\frac{1}{e+1}x^{e+1}$

7. zepdrix

How bout the other term, integral of e^x?

8. AmTran_Bus

Isn't it just e^x?

9. zepdrix

good good good.

10. zepdrix

$\Large\rm \int\limits_0^1 x^e+e^x dx=\quad\frac{1}{e+1}x^{e+1}+e^x\quad |_0^1$

11. zepdrix

So then just deal with the limits, ya? :d

12. AmTran_Bus

I thought the integral of x^3 like you did above was x^4/4?

13. zepdrix

$\Large\rm \frac{x^4}{4}=\frac{1}{4}x^4$

14. AmTran_Bus

Ok. Yes, I can apply the limits. I just wanted to get the core idea of the problem. Thanks.

15. zepdrix

no probs

16. zepdrix

Yah you can rewrite your x term like that if you're more comfortable with it:$\Large\rm \frac{1}{e+1}x^{e+1}=\frac{x^{e+1}}{e+1}$