Question

please integrate for me (cosec x)/(cosecx-sinx) dx

Answer 1

∫ csc(x)dx
=-ln[csc(x)+cot(x)]+C answer//

Answer 2

\[\begin{align}
\int \frac{\csc{x}}{\csc{x}-\sin{x}}\ dx&=\int\frac{1}{1-\sin^2{x}}\ dx\\
&=\int\frac{1}{\cos^2{x}}\ dx \\
&=\int \sec^2{x}\ dx\\
&=\tan^2{x} + C
\end{align}\]

Answer 3

\[ ∫ sec^2 xdx\] is tanx +C :)

Answer 4

Oops. My fingers are getting ahead of my mind. =))

Answer 5

the answer is tanx + c how u get the ans callisto ? help me please

Answer 6

@blockcolder 's working is correct.
The only problem is that he typed so fast that he mistyped the answer for the last step.

Answer 7

thanks a lot guys . but how you conclude cosecx/ (cscx-sinx) equal to 1/ (1-sinx) ?

Answer 8

I multiplied numerator and denominator by sin(x).

Answer 9

oh thts mean we can multiple it by anything to simplify it ?

Answer 10

cscx/ (cscx-sinx)
= csc x / [(1/sinx) - sinx]
= cscx / [(1-sin^2 x)/sinx]
= cscx (sinx) / (1-sin^2 x)
= 1/(cos^2 x)
= (sec^2 x)

Answer 11

Yes. :D

Answer 12

ok got it. thanks again :)

Answer 13

welcome :)

Answer 14

You're welcome. :D