What is the integral of (3cos(x)-4sin(x)+5sec^2(x)) ?

The integral of (3cos(x)-4sin(x)+5sec^2(x)) is 3sin(x)+4cos(x)+5tan(x)+C

Popular >

integral of (3cos(x)-4sin(x)+5sec^2(x))

\int (3 cos (x) - 4 sin (x) + 5 sec^{2} (x)) d x

3 sin (x) + 4 cos (x) + 5 tan (x) + C

Solution steps

\int 3 cos (x) - 4 sin (x) + 5 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 cos (x) d x - \int 4 sin (x) d x + \int 5 sec^{2} (x) d x

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

\int 4 sin (x) d x = - 4 cos (x)

\int 5 sec^{2} (x) d x = 5 tan (x)

= 3 sin (x) - (- 4 cos (x)) + 5 tan (x)

Simplify

= 3 sin (x) + 4 cos (x) + 5 tan (x)

Add a constant to the solution

= 3 sin (x) + 4 cos (x) + 5 tan (x) + C

\int sec^{4} (y) tan^{3} (y) d y

\int \frac{2 x ^{2} + x ^{4}}{- 4 x ^{2}} d x

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

\int (x + 4) arctan (\frac{x}{2}) d x

\int \frac{2}{x ^{3} x ^{4} - 36} d x

What is the integral of (3cos(x)-4sin(x)+5sec^2(x)) ?
The integral of (3cos(x)-4sin(x)+5sec^2(x)) is 3sin(x)+4cos(x)+5tan(x)+C