Question

How to integrate 3^(x+3^x)

Answer 1

Try U-sub

Answer 2

Okay sure

Answer 3

splitting it up first might help

3^(x+3^x) = 3^x * 3^(3^x)
= 3^x * 3^(3x)

Answer 4

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

Answer 5

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

Answer 6

Continue

Answer 7

@welshfella

\[\large 3^{(3^x)}~~ \ne~~ 3^{3x}\]

right

Answer 8

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

Answer 9

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

Answer 10

Thank you everyone~

Answer 11

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

Answer 12

@rational - right!