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Mastermind01 said:You don't need by parts to do this. You can use a simple substitution.
[tex]\int 3^x ln 3 dx[/tex]
Let [itex]u = 3^x[/itex] , then [itex] du = 3^x ln 3 dx[/itex]
The integral becomes [tex]\int du [/tex] Integrate and substitute u back.
Electgineer99 said:
- The equation is 3^xlog3
it is base 10, but will it make any difference if it is base 10 or any other bases?Mastermind01 said:That's what I wrote, or do you mean to say it's base 10?
Electgineer99 said:it is base 10, but will it make any difference if it is base 10 or any other bases?
That integrand is 3 times ln(3) .Electgineer99 said:∫3×ln3.dx
u=3× dx=du/ln(3).3×
∫u.ln(3).du/ln(3).3×
ln(3) canceled each other.
∫u.du/3×
⅓×∫u.du
⅓×.u²/2
Then I would substitute u=3×
Am I right with this?
I believe that you mean 3x or write 3^x .Electgineer99 said:Okay I got it now, u° equal 1, so the answer is 3×.
Integration by parts is a mathematical method used to find the integral of a product of two functions. It involves breaking down the original integral into two parts and using the product rule of differentiation to simplify it.
Integration by parts is usually used when the integral involves a product of functions that cannot be easily integrated using other techniques, such as substitution or trigonometric identities.
The formula for integration by parts is ∫u dv = uv - ∫v du, where u and v are the two functions in the original integral and du and dv are their respective differentials.
A common way to choose the functions is to remember the acronym "LIATE", which stands for Logarithmic, Inverse trigonometric, Algebraic, Trigonometric, and Exponential. The function that comes first in this order is usually chosen as u, while the other function is chosen as dv. However, this may not always work and other techniques may need to be used.
Yes, integration by parts can be used for definite integrals. The same formula applies, but the limits of integration must be applied to both terms in the formula, and the resulting equation can then be solved for the definite integral.