What is the integral of 3sin(x)-2sec^2(x) ?

The integral of 3sin(x)-2sec^2(x) is -3cos(x)-2tan(x)+C

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integral of 3sin(x)-2sec^2(x)

\int 3 sin (x) - 2 sec^{2} (x) d x

- 3 cos (x) - 2 tan (x) + C

Solution steps

\int 3 sin (x) - 2 sec^{2} (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 3 sin (x) d x - \int 2 sec^{2} (x) d x

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

\int 2 sec^{2} (x) d x = 2 tan (x)

= - 3 cos (x) - 2 tan (x)

Add a constant to the solution

= - 3 cos (x) - 2 tan (x) + C

\int \frac{x + 1}{x ^{3} + 3 x ^{2} - 10 x} d x

\int csc (\frac{6}{7}) x d x

\int π sin (π x) (3 + 2 cos (π x))^{3} d x

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

\int (2 x + 3)^{9} d x

What is the integral of 3sin(x)-2sec^2(x) ?
The integral of 3sin(x)-2sec^2(x) is -3cos(x)-2tan(x)+C