thharrimw said:T know my anwser is right becose i checked it but dose anyone know a faster way to find the integral of x^8
x^2+26x+48
other than long division and then partial fractions?
HallsofIvy said:You mean
[tex]\frac{x^8}{x^2+ 26x+ 48}[/tex]
(it looked like a polynomial to me!)
No, there is not a simpler or faster way to do that.
The formula for finding the integral of x^8 + 26x + 48 is ∫(x^8 + 26x + 48)dx = (1/9)x^9 + 13x^2 + 48x + C, where C is the constant of integration.
The most efficient method for solving the integral of x^8 + 26x + 48 is by using the Power Rule, which states that ∫x^n dx = (1/(n+1))x^(n+1) + C. This method allows for a quicker and simpler solution compared to other integration techniques.
Yes, the integral of x^8 + 26x + 48 can be solved using substitution. By letting u = x^8 + 26x + 48, the integral can be rewritten as ∫u/8 du, which can then be solved using the Power Rule.
The integral of x^8 + 26x + 48 can be solved using integration by parts by choosing u = x^8 and dv = (26x + 48)dx. This will result in du = 8x^7 dx and v = (13x^2 + 48x). Plugging these values into the integration by parts formula, the integral can be solved as ∫x^8 dx = (1/9)x^9 + 13x^2 + 48x - ∫(13x^2 + 48x)(8x^7)dx. This new integral can then be solved using the Power Rule and the process can be repeated until the integral is fully solved.
Yes, there are faster solutions for solving the integral of x^8 + 26x + 48. One such method is using partial fractions, which involves breaking down the integrand into simpler fractions that can then be integrated individually. Another method is using the trapezoidal rule, which approximates the integral by breaking it down into smaller trapezoids and summing their areas. This method is particularly useful for solving integrals that cannot be solved using traditional techniques.