- #1
lord12
- 9
- 0
integral of (e^(2x))(cos3x)dx
I get 1/2e^(2x)sin2x - 3/2integral(e^(2x)cos3xdx)
what do i do next?
I get 1/2e^(2x)sin2x - 3/2integral(e^(2x)cos3xdx)
what do i do next?
Gib Z said:It occurs often, and many times more than just once. In fact many go on an infinite number of applications.
Integration by parts is a mathematical method used to find the integral of a product of two functions. It is based on the product rule of differentiation and is particularly useful for solving integrals involving polynomials, exponential functions, and trigonometric functions.
Integration by parts is typically used when the integral involves a product of two functions that cannot be easily simplified or evaluated using other methods, such as substitution or partial fractions. It is also useful for solving integrals that involve logarithmic functions or inverse trigonometric functions.
The formula for integration by parts is ∫udv = uv - ∫vdu, where u and v are the two functions being multiplied together and du and dv are their respective differentials. This formula is derived from the product rule of differentiation.
When using integration by parts, u and dv are chosen based on a specific order of preference known as the "ILATE" rule. "ILATE" stands for Inverse trigonometric functions, Logarithmic functions, Algebraic functions, Trigonometric functions, and Exponential functions. The function that falls first in this order is chosen as u, while the other function is chosen as dv.
Yes, there are a few special cases for integration by parts. One is when the integrand contains a polynomial multiplied by a power of x, in which case u can be chosen as the polynomial and dv as the power of x. Another special case is when the integrand contains a logarithmic function multiplied by a power of x, in which case u can be chosen as the logarithmic function and dv as the power of x.