Integration by Parts
Integration by Parts is a fundamental technique in calculus used to evaluate the integral of a product of functions. By breaking down a complex integral into simpler parts and applying the integration formula, Integration by Parts enables the computation of integrals that are otherwise challenging to solve directly. This method involves selecting one function to differentiate and another to integrate, ultimately transforming the original integral into a more manageable form. With its application, mathematicians and scientists can solve a wide range of integrals encountered in various fields, from physics to engineering and beyond.
Questions
- Find # I = int \ lnx/x^2 \ dx #?
- How do you integrate #int x cos sqrtx dx # using integration by parts?
- How do you integrate #int 3 xln x^3 dx # using integration by parts?
- How do you integrate #x^2 e^-5x dx#?
- What is the general method for integrating by parts?
- How do you integrate #intx cos 2x dx#?
- How do you integrate #int x^nlnx# by integration by parts method?
- How do you find the integral #ln x / x#?
- What is the antiderivative of #(ln^6 x)/x#?
- How can I use integration by parts to find #int_{0}^{5}te^{-t}dt#?
- Let #f_n(x) = sum_(r=1)^n \ sin^2(x)/(cos^2(x/2)-cos^2(( (2r+1)x)/2) ) # and #g_n(x) = prod_(k=1)^n f_k(x) #. If #I_n=int_0^pi (f_n(x))/(g_n(x)) dx # show that #sum_(k=1)^n I_k = Kpi#, and find #K#?
- How do integrate #int e^(cos)(t) (sin 2t) dt# between a = 0, #b = pi#?
- How do you integrate #int x^2 cos3 x dx # using integration by parts?
- How do you integrate #int lnx/x^2# by integration by parts method?
- How do you integrate #int x^3ln(5x)# by integration by parts method?
- How do you evaluate the integral #int arctansqrtx#?
- How do you integrate #xln(1+x) dx#?
- How to know when to use integration by substitution vs. integration by parts?
- How do you integrate #int sin^-1x# by integration by parts method?
- How do you integrate #int x^3 ln x^2 dx # using integration by parts?