What is the integral of 7(sec(x))^2-4sin(x) ?

The integral of 7(sec(x))^2-4sin(x) is 7tan(x)+4cos(x)+C

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integral of 7(sec(x))^2-4sin(x)

\int 7 (sec (x))^{2} - 4 sin (x) d x

7 tan (x) + 4 cos (x) + C

Solution steps

\int 7 (sec (x))^{2} - 4 sin (x) d x

Simplify

= \int 7 sec^{2} (x) - 4 sin (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 7 sec^{2} (x) d x - \int 4 sin (x) d x

\int 7 sec^{2} (x) d x = 7 tan (x)

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

= 7 tan (x) - (- 4 cos (x))

Simplify

= 7 tan (x) + 4 cos (x)

Add a constant to the solution

= 7 tan (x) + 4 cos (x) + C

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

\frac{d}{d x} (sin (π))

\frac{d}{d x} ((x^{3} + 2) e^{x})

y^{^{''}} - 2 y = 5

\int \frac{( 3 in x - 5 ) ^{4}}{x} d x

What is the integral of 7(sec(x))^2-4sin(x) ?
The integral of 7(sec(x))^2-4sin(x) is 7tan(x)+4cos(x)+C