What is the integral of 10cos(x)tan(x)-4sin(x)cot(x) ?

The integral of 10cos(x)tan(x)-4sin(x)cot(x) is -10cos(x)-4sin(x)+C

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integral of 10cos(x)tan(x)-4sin(x)cot(x)

\int 10 cos (x) tan (x) - 4 sin (x) cot (x) d x

- 10 cos (x) - 4 sin (x) + C

Solution steps

\int 10 cos (x) tan (x) - 4 sin (x) cot (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 10 cos (x) tan (x) d x - \int 4 sin (x) cot (x) d x

\int 10 cos (x) tan (x) d x = - 10 cos (x)

\int 4 sin (x) cot (x) d x = 4 sin (x)

= - 10 cos (x) - 4 sin (x)

Add a constant to the solution

= - 10 cos (x) - 4 sin (x) + C

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\int (1 - cos^{2} (x)) sin (x) cos^{2} (x) d x

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\int 9 sec (x) d x

What is the integral of 10cos(x)tan(x)-4sin(x)cot(x) ?
The integral of 10cos(x)tan(x)-4sin(x)cot(x) is -10cos(x)-4sin(x)+C