The square root is a #1/2# power, which can be brought from the logarithm rule: log(A^B)=Blog(A)#. Type in any integral to get the solution, steps and. Save to Notebook Free integral calculator - solve indefinite, definite and multiple integrals with all the steps. Even though derivatives are fairly straight forward, integrals are. Integration is the inverse of differentiation. However, we can simplify it rather sneakily: Advanced Math Solutions Integral Calculator, the basics. To remedy this, add absolute value bars.) This is not the case in the original function, but the trigonometry introduced this issue.
This almost could be a final answer, but there is one problem, which is that #sqrt(x^2-3)# in the answer restricts the domain, in that we see that the domain excludes #-sqrt3 < x < sqrt3#. Note that #sectheta=x/sqrt3#, thus we have a right triangle where #x# is the hypotenuse, #sqrt3# is the side adjacent to #theta#, and the opposite side is #sqrt(x^2-3)#. #I=1/sqrt3int(secthetatanthetad theta)/tan^2theta=1/sqrt3int(secthetad theta)/tantheta=1/sqrt3int1/costheta(costheta/sintheta)d theta=1/sqrt3intcscthetad theta#
#I=int(sqrt3secthetatanthetad theta)/(3sec^2theta-3)=sqrt3/3int(secthetatanthetad theta)/(sec^2theta-1)# Let #x=sqrt3sectheta#, implying that #dx=sqrt3secthetatanthetad theta#:
