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

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

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

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

tan (x) + cos (x) + C

Solution steps

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

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

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

= tan (x) - (- cos (x))

Simplify

= tan (x) + cos (x)

Add a constant to the solution

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

\int \frac{1}{3} e^{3 x} d x

\int_{0}^{\frac{π}{2}} cos^{5} (6 x) d x

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

\frac{d}{d x} (arctan (x) + 2 x - 2)

y = x^{\frac{15}{16}}

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