IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

Terminator.HCV

integratn[tanx dx/(1+sinx)] urgent

mukundmadhav

multiply and divide by 1-sinx. Write everything in terms of tanx and secx.. Put either of the two as t and solve using standard formulae.

Terminator.HCV

oh! yes i forgot abt that technique!!!!!!!!!!!
Thankx!!

Terminator.HCV

Hey! its not coming that way!!!!!!!!!!!!
Please advice ANYBODY.....................

studyid

See the sum is best solved by trigonometry ..

but if u dont want to solve it by trigonometry then here's an aliter :

$\int\frac{tanx}{1-sinx} dx\\Put\;tan(\frac{x}{2}) = t\\Hence\;dx = \frac{2dt}{1+{t}^{2}}\\tanx=\frac{2t}{1-{t}^{2}}\;and\;sinx=\frac{2t}{1+{t}^{2}}$

Hence given integral becomes,

$\int\frac{(\frac{2t}{1-{t}^{2}})(\frac{2dt}{1+{t}^{2}})}{1+\frac{2t}{1+{t}^{2}}}$

$= \int\frac{dt}{(1+t)^{2}(1-{t}^{2})}$

Now proceed the integral becomes simpler to obtain.