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

The integral of sec^2(pix) is 1/pi tan(pix)+C

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integral of sec^2(pix)

\int sec^{2} (π x) d x

\frac{1}{π} tan (π x) + C

Solution steps

\int sec^{2} (π x) d x

Rewrite using trig identities

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

\int 1 d x = x

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

= x - x + \frac{1}{π} tan (π x)

Simplify

= \frac{1}{π} tan (π x)

Add a constant to the solution

= \frac{1}{π} tan (π x) + C

\int_{- 1}^{1} t (1 - t)^{2} d t

x \to 0 lim (x^{3} ln (x^{2} + 1))

n = 1 \sum \infty \frac{( - 3 ) ^{n - 1}}{8 ^{n}}

\frac{\partial}{\partial x} (4 (x - 1)^{2})

n = 1 \sum \infty n sin (\frac{1}{n})

What is the integral of sec^2(pix) ?
The integral of sec^2(pix) is 1/pi tan(pix)+C