you know that the derivative of a^x is a^xlna. Therefore, the derivative of 3^x is 3^xln3. In the case of 3^2x it is 3^2xln3(2), it is multiplied by 2 because you have to do the chain rule as 3 is to a power of x but in this case the coefficient of x isn't 1, but rather 2 (and the differential of 2x is 2 so you have to take that into account). Knowing this you can see that 3^2xln3(2) is similar to 3^2x (what you are trying to integrate, but not the same. You have two constants there (ln3) and 2 which you don't want. You will want to get rid of them by going by to the 3^2x line and putting a 1/ln3 * 1/2 there so that when you differentiate (1/2ln3)*3^2x the 2 will cancel with the 1/2 and the 1/ln3 will cancel with the ln3. If that doesn't make sense I can maybe explain that differently.
you know that the derivative of a^x is a^xlna. Therefore, the derivative of 3^x is 3^xln3. In the case of 3^2x it is 3^2xln3(2), it is multiplied by 2 because you have to do the chain rule as 3 is to a power of x but in this case the coefficient of x isn't 1, but rather 2 (and the differential of 2x is 2 so you have to take that into account). Knowing this you can see that 3^2xln3(2) is similar to 3^2x (what you are trying to integrate, but not the same. You have two constants there (ln3) and 2 which you don't want. You will want to get rid of them by going by to the 3^2x line and putting a 1/ln3 * 1/2 there so that when you differentiate (1/2ln3)*3^2x the 2 will cancel with the 1/2 and the 1/ln3 will cancel with the ln3. If that doesn't make sense I can maybe explain that differently.
the c3 formula states that a^x is e^xlna so in my case it'll be e^2xln3
you know that the derivative of a^x is a^xlna. Therefore, the derivative of 3^x is 3^xln3. In the case of 3^2x it is 3^2xln3(2), it is multiplied by 2 because you have to do the chain rule as 3 is to a power of x but in this case the coefficient of x isn't 1, but rather 2 (and the differential of 2x is 2 so you have to take that into account). Knowing this you can see that 3^2xln3(2) is similar to 3^2x (what you are trying to integrate, but not the same. You have two constants there (ln3) and 2 which you don't want. You will want to get rid of them by going by to the 3^2x line and putting a 1/ln3 * 1/2 there so that when you differentiate (1/2ln3)*3^2x the 2 will cancel with the 1/2 and the 1/ln3 will cancel with the ln3. If that doesn't make sense I can maybe explain that differently.