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

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

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

\int sin (x) 1 + cos (x) d x

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

Solution steps

\int sin (x) \cdot 1 + cos (x) d x

Simplify

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

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

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

= - cos (x) + sin (x)

Add a constant to the solution

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

\int \frac{x}{x ^{2} - 3 x} d x

\int (10 x + 7) d x

\int \frac{1}{2 + cos ( θ )} d θ

\int 2 x (1 - x) d x

\int \frac{x ^{2} - 16}{x ^{2}} d x

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