Integral Calculus> indefinite integration...

[(tanx)/x].dx

deepsekhar choudhury , 13 Years ago

Grade

3 Answers

Parth Shrivastava

Last Activity: 13 Years ago

This can be integrated by integration by parts
let 1/x=d v
then logx dx =v on integrating
let tanx=u
sec^2xdx=du
∫ udv = uv- ∫ vdu = logxtanx- ∫logxsec^2xdx
so ∫tanx/x dx= logxtanx- ∫ logx sec^2xdx------ (1)

now consider the second term in the RHS
∫ logx sec^2x dx, again applying by parts technique
let u= logx , du= 1/xdx ∫sec^2x dx= dv , v= tanx on integrating

so this becomes logxtanx- ∫tanx/x dx

substituting in eqn (1)
integral tanx/x dx= logxtanx+logxtan- ∫tanx/xdx
2 ∫tanx/x dx= 2logxtanx

so ∫tanx/x =logx tanx+c

Ans

jbdjhsfgbr gnjsndvjesr

Last Activity: 13 Years ago

its a very easy question... try teaching something more useful to students....

Anantha padmanabam

Last Activity: 9 Years ago

let 1/x=d v
then logx dx =v on integrating
let tanx=u
sec^2xdx=du
∫ udv = uv- ∫ vdu = logxtanx- ∫logxsec^2xdx
so ∫tanx/x dx= logxtanx- ∫ logx sec^2xdx------ (1)

now consider the second term in the RHS
∫ logx sec^2x dx, again applying by parts technique
let u= logx , du= 1/xdx ∫sec^2x dx= dv , v= tanx on integrating

so this becomes logxtanx- ∫tanx/x dx

substituting in eqn (1)

After substituting in eqn 1 u will get logx tanx - logx tanx + internal (tanx/x)

Which will give back the question