What is the integral of cos(x)(tan(x)-3) ?

The integral of cos(x)(tan(x)-3) is -cos(x)-3sin(x)+C

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integral of cos(x)(tan(x)-3)

\int cos (x) (tan (x) - 3) d x

- cos (x) - 3 sin (x) + C

Solution steps

\int cos (x) (tan (x) - 3) d x

Rewrite using trig identities

= \int sin (x) - 3 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 3 cos (x) d x

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

\int 3 cos (x) d x = 3 sin (x)

= - cos (x) - 3 sin (x)

Add a constant to the solution

= - cos (x) - 3 sin (x) + C

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\int 3 x^{3} e^{3 x^{2}} d x

What is the integral of cos(x)(tan(x)-3) ?
The integral of cos(x)(tan(x)-3) is -cos(x)-3sin(x)+C