Question

solve the integration f(sinx+cosx)^2dx

Answer 1

is this
\[\int(\sin(x)+\cos(x))^2dx\]?

Answer 2

yes

Answer 3

square and get
\[\sin^2(x)+\cos^2(x)+2\sin(x)\cos(x)=1+\sin(2x)\] then it should be ok

Answer 4

\[\int 1dx+\int\sin(2x)dx\]

Answer 5

can u tell me easy method to sove like this integrations?

Answer 6

not sure what you mean. the original integral wants you to square.

Answer 7

ok

Answer 8

if you mean how to solve
\[\int\sin(2x)dx\] you visualize what you would get if you take the derivative of
\[\cos(2x)\] you would get
\[-2\sin(2x)\] but you want just
\[\sin(2x)\] so your integral is
\[-\frac{1}{2}\cos(2x)\]

Answer 9

ok ok

Answer 10

thanks my dear

Answer 11

\[\int\limits_{\sec^2xcosec^2x}^{dx}\]