## anonymous one year ago How to integrate 3^(x+3^x)

1. .Sam.

Try U-sub

2. anonymous

Okay sure

3. welshfella

splitting it up first might help 3^(x+3^x) = 3^x * 3^(3^x) = 3^x * 3^(3x)

4. anonymous

So the integral of 3^x is 3^x / ln(3)

5. .Sam.

$\int\limits 3^{x+3^x}dx = \int\limits 3^x \times 3^{3^x} dx$ Let $u=3^x \\ \\ du=3^xln(3)dx$ $\int\limits 3^u\frac{1}{\ln(3)}du$

6. .Sam.

Continue

7. rational

@welshfella $\large 3^{(3^x)}~~ \ne~~ 3^{3x}$ right

8. anonymous

Oh yes! I got it! The answer is 3^(3^x) / (ln(3))^2 + C

9. anonymous

So when I look at these types of problems I should look at splitting up the problem and if I can u-sub something. Thanks

10. anonymous

Thank you everyone~

11. .Sam.

Yes always think of U-sub first, then followed by other methods if you can't U-sub

12. welshfella

@rational - right!