What is the integral of-cos(x)tan(x) ?

The integral of-cos(x)tan(x) is cos(x)+C

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integral of-cos(x)tan(x)

\int - cos (x) tan (x) d x

cos (x) + C

Solution steps

\int - cos (x) tan (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Express with sin, cos

= - \int sin (x) d x

Use the common integral:

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

= - (- cos (x))

Simplify

= cos (x)

Add a constant to the solution

= cos (x) + C

\int x (1 + x^{2}) arctan (x) d x

\int \frac{1}{9 x + 2} d x

\int - 4 x cos (\frac{x}{2}) d x

\int 4 x - 6 x^{2} d x

\int x \cdot tan (\frac{x}{3}) d x