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

The integral of (sec^2(pix)-sqrt(x)) is 1/pi tan(pix)-2/3 x^{3/2}+C

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

\int (sec^{2} (π x) - x) d x

\frac{1}{π} tan (π x) - \frac{2}{3} x^{\frac{3}{2}} + C

Solution steps

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

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

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

= \frac{1}{π} tan (π x) - \frac{2}{3} x^{\frac{3}{2}}

Add a constant to the solution

= \frac{1}{π} tan (π x) - \frac{2}{3} x^{\frac{3}{2}} + C

\frac{\partial}{\partial x} ((\frac{y x}{z w})^{\frac{1}{2}})

\frac{d}{d x} (\frac{4 - x e ^{x}}{x + e ^{x}})

n = 1 \sum \infty \frac{cos ( nπ )}{n ^{2}}

x \to 2 lim (\frac{x + 47 - 7}{5 x - 10})

\frac{\partial}{\partial x} (y^{5} sin (6 x))

What is the integral of (sec^2(pix)-sqrt(x)) ?
The integral of (sec^2(pix)-sqrt(x)) is 1/pi tan(pix)-2/3 x^{3/2}+C