How do you integrate #int [(x-1) / (cos^2 x)]dx#? Calculus Introduction to Integration Integrals of Trigonometric Functions 1 Answer maganbhai P. Jun 2, 2018 #I=(x-1)tanx-ln|secx|+c# Explanation: Here, #I=int[(x-1)/cos^2x]dx# #int(x-1)sec^2xdx# #"Using "color(blue)"Integration by Parts :"# #color(blue)(intu*vdx=uintvdx-int(u'intvdx)dx# Let, #u=x-1 and v=sec^2x=>u'=1 and intvdx=tanx# So, #I=(x-1)*tanx-int1*tanxdx# #I=(x-1)tanx-ln|secx|+c# Answer link Related questions How do I evaluate the indefinite integral #intsin^3(x)*cos^2(x)dx# ? How do I evaluate the indefinite integral #intsin^6(x)*cos^3(x)dx# ? How do I evaluate the indefinite integral #intcos^5(x)dx# ? How do I evaluate the indefinite integral #intsin^2(2t)dt# ? How do I evaluate the indefinite integral #int(1+cos(x))^2dx# ? How do I evaluate the indefinite integral #intsec^2(x)*tan(x)dx# ? How do I evaluate the indefinite integral #intcot^5(x)*sin^4(x)dx# ? How do I evaluate the indefinite integral #inttan^2(x)dx# ? How do I evaluate the indefinite integral #int(tan^2(x)+tan^4(x))^2dx# ? How do I evaluate the indefinite integral #intx*sin(x)*tan(x)dx# ? See all questions in Integrals of Trigonometric Functions Impact of this question 1595 views around the world You can reuse this answer Creative Commons License