What is #int_1^(e^(pi/4)) 4/(x(1+(lnx)^2))dx#? Calculus Techniques of Integration Integration by Trigonometric Substitution 1 Answer maganbhai P. Mar 16, 2018 #4tan^-1(pi/4)# Explanation: #I=int_1^(e^(pi/4))4/(x(1+(lnx)^2))dx# Let, #lnx=u=>1/x*dx=du# #x=1=>u=ln1=>u=0and# #x=e^(pi/4)=>u=lne^(pi/4)=>u=pi/4# #:.I=int_0^(pi/4)4/(1+u^2)du=[4tan^-1u]_0^(pi/4)# #:.I=4[tan^-1(pi/4)-tan^-1(0)]=4[tan^-1(pi/4)-0]# #:.I=4tan^-1(pi/4)# Answer link Related questions How do you find the integral #int1/(x^2*sqrt(x^2-9))dx# ? How do you find the integral #intx^3/(sqrt(x^2+9))dx# ? How do you find the integral #intx^3*sqrt(9-x^2)dx# ? How do you find the integral #intx^3/(sqrt(16-x^2))dx# ? How do you find the integral #intsqrt(x^2-1)/xdx# ? How do you find the integral #intsqrt(x^2-9)/x^3dx# ? How do you find the integral #intx/(sqrt(x^2+x+1))dx# ? How do you find the integral #intdt/(sqrt(t^2-6t+13))# ? How do you find the integral #intx*sqrt(1-x^4)dx# ? How do you prove the integral formula #intdx/(sqrt(x^2+a^2)) = ln(x+sqrt(x^2+a^2))+ C# ? See all questions in Integration by Trigonometric Substitution Impact of this question 1757 views around the world You can reuse this answer Creative Commons License