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

The integral of sqrt(x)-sec^2(x) is 2/3 x^{3/2}-tan(x)+C

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

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

\frac{2}{3} x^{\frac{3}{2}} - tan (x) + C

Solution steps

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

\int x d x = \frac{2}{3} x^{\frac{3}{2}}

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

= \frac{2}{3} x^{\frac{3}{2}} - tan (x)

Add a constant to the solution

= \frac{2}{3} x^{\frac{3}{2}} - tan (x) + C

What is the integral of sqrt(x)-sec^2(x) ?
The integral of sqrt(x)-sec^2(x) is 2/3 x^{3/2}-tan(x)+C