What is the integral of sec^3(pi)x ?

The integral of sec^3(pi)x is -(x^2)/2+C

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integral of sec^3(pi)x

\int sec^{3} (π) x d x

- \frac{x ^{2}}{2} + C

Solution steps

\int sec^{3} (π) x d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= sec^{3} (π) \cdot \int x d x

sec^{3} (π) = - 1

= (- 1) \cdot \int x d x

Apply the Power Rule

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

Simplify

= - \frac{x ^{2}}{2}

Add a constant to the solution

= - \frac{x ^{2}}{2} + C