- #1
barksdalemc
- 55
- 0
I did a few problems in integration by parts. There are two that I just can't seem to get. I've tried every type of subsitution or part I can think of.
1. e^sqrt(x)
2. sin (ln x)
1. e^sqrt(x)
2. sin (ln x)
Integration by substitution involves replacing a variable in an integral with a new variable, while integration by parts involves splitting an integral into two parts and applying a specific formula. Substitution is typically used when the integrand (the function inside the integral) is composed of a single function, while integration by parts is used when the integrand is composed of two functions.
You can use integration by substitution when the integrand consists of a single function, and the derivative of this function is also present in the integrand. This is known as the "u-substitution" method, where the new variable u is substituted in place of the original variable in the integral.
The steps for integration by substitution are as follows:
Integration by parts is useful when the integrand consists of two functions, and one of those functions has a known antiderivative. This method can also be used when the integrand involves products of functions, as well as when the integrand involves trigonometric functions.
The formula for integration by parts is:
∫ u(x)v'(x) dx = u(x)v(x) - ∫ v(x)u'(x) dx
Where u(x) is the first function, v'(x) is the derivative of the second function, v(x) is the antiderivative of v'(x), and u'(x) is the derivative of u(x).