Integration!

Calculus Level 2

$\int { \frac { \cos { (2x) } }{ \cos { (x)+\sin { (x) } } } \, dx = \, ? }$

\sin(2x)-\cos(2x)+C

\cos(2x)-\sin(2x)+C

\sin(x)-\cos(x)+C

\sin(x)+\cos(x)+C

1 solution

Mahmoud Mustafa
Jan 5, 2016

$\int { \frac { \cos { (2x) } }{ \cos { (x)+\sin { (x) } } } \, dx } \\ =\int { \frac { \cos^2(x)- \sin^2 (x) }{ \cos { (x) } +\sin { (x) } } \, dx } \\ =\int { \frac { (\cos(x)+\sin(x))(\cos(x)-\sin(x)) }{ \cos(x)+\sin(x) } \, dx } \\ =\int { \cos(x)-\sin(x) \, dx } \\ =~\large\boxed{\sin(x)+\cos(x)+C}$

Good solution! I have made your solution easier to read by making a new line for each step. Also note that when writing trigonometric functions in LaTeX you can use \cos^2 and \sin^2 instead of {\cos(x)}^{2} .

Michael Fuller - 5 years, 5 months ago

lol I just turned the $\sin(x)+\cos(x)$ in 1 and it get a lot harder

Pedro Henrique - 5 years, 5 months ago

Integration!

1 solution

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