What is the integral of (1+sin(2x))/(sin(x)+cos(x)) ?

The integral of (1+sin(2x))/(sin(x)+cos(x)) is sin(x)-cos(x)+C

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integral of (1+sin(2x))/(sin(x)+cos(x))

\int \frac{1 + sin ( 2 x )}{sin ( x ) + cos ( x )} d x

sin (x) - cos (x) + C

Solution steps

\int \frac{1 + sin ( 2 x )}{sin ( x ) + cos ( x )} d x

Rewrite using trig identities

= \int cos (x) + sin (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int cos (x) d x + \int sin (x) d x

\int cos (x) d x = sin (x)

\int sin (x) d x = - cos (x)

= sin (x) - cos (x)

Add a constant to the solution

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

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\int \frac{- 1}{1 - ( 4 x + 1 ) ^{2}} d x

What is the integral of (1+sin(2x))/(sin(x)+cos(x)) ?
The integral of (1+sin(2x))/(sin(x)+cos(x)) is sin(x)-cos(x)+C