Integrals of Rational Functions
Integrals of rational functions play a fundamental role in calculus, offering powerful tools for solving complex mathematical problems. These functions, expressed as ratios of polynomials, can be challenging to integrate directly but can often be simplified using techniques such as partial fraction decomposition. Through careful manipulation and application of integration rules, these integrals unveil crucial insights into the behavior of functions, aiding in the analysis of various phenomena across fields such as physics, engineering, and economics. Understanding their properties enables practitioners to tackle a wide range of mathematical problems efficiently and effectively.
Questions
- How do you integrate #x/(x-6)#?
- How do you find the integral of #(6x+1)/(x^2+2x+3)#?
- What is #int (x^2-5x+4 ) / (x^3-2x +4 )#?
- How do you evaluate the integral #int x/(root3(x^2-1))#?
- What is #int (x^3-2x^2+6x+9 ) / (-x^2- x +3 )#?
- How do you find the indefinite integral of #int 1/(x+1)#?
- What is the antiderivative of #(x+2)/(x+1)#?
- How do you find the antiderivative of #1/x^2#?
- What is #int (-2x^3-x^2+x+2 ) / (3x^2+2x +3 )#?
- How do you evaluate the integral #intdx/(2x+3)#?
- How do you integrate #(xdx)/(x^2+2)^3# which has the upper and lower limits, 2 and 1 ?
- What is #int (-3x^3+4 ) / (5x^2-2x +1 )#?
- What is the antiderivative of #x/(x^2+1) #?
- What is #int (2x^3-3x^2-2x-3 ) / (-8x^2+ 2 x -2 )#?
- What is the Integral of #(x+1)/x dx#?
- How do you integrate #x^3/(1+x^2)#?
- How do you integrate #(-2x)/((x^2+2x+2)^2) #?
- How do you integrate #(x^2 + 2x -5) / [(x - 2)*(x+1)*(x^2+1)]#?
- #int(x^2+x+2)/{(x-1)(x-2)}dx# with respect to x ?
- How do you integrate #(5/sqrt x) dx#?