Question

Find the indefinite integral of cos(x)(sin(sinx))

Answer 1

@eliassaab

Answer 2

\[I=\int\limits \cos x \sin \left( \sin x \right)dx\]
put sin ~x=t
cos~`x~dx=dt
\[I=\int\limits \sin t~dt=-\cos ~t+c\]
replace the value of t.

Answer 3

@surjithayer which method did you use? integration by parts or what?

Answer 4

no integration by parts ,only substitution.

Answer 5

@surjithayer Thanks very much. Btw do you know how to find the indefinite integral of sqrt(1-sinx)?

Answer 6

\[I=\int\limits \sqrt{1-\sin x}~dx=\int\limits \left(\sqrt{\cos ^2\frac{ x }{ 2 }+\sin ^2\frac{ x }{2 }-2\sin \frac{ x }{ 2 }\cos \frac{ x }{ 2 }}\right)dx+c\]
\[=\int\limits \left( \cos \frac{ x }{ 2 }-\sin \frac{ x }{ 2} \right)dx+c\]
i think now you can complete it.

Answer 7

i am going to dinner.

Answer 8

@surjithayer can you please explain to me how 1-sinx = to cos^2x/2 + sin^2....... the whole thing under the root?

Answer 9

\[\cos ^2x+\sin ^2x=1,\sin 2x=2\sin x \cos x\]

Answer 10

okay and then......

Answer 11

\[\left( a-b \right)^2=a^2+b^2-2ab\]