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

The integral of sec(h^3)x is 1/2 x^2sec(h^3)+C

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integral of sec(h^3)x

\int sec (h^{3}) x d x

\frac{1}{2} x^{2} sec (h^{3}) + C

Solution steps

\int sec (h^{3}) x d x

Take the constant out:

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

= sec (h^{3}) \cdot \int x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

= sec (h^{3}) \frac{x ^{2}}{2}

Simplify

sec (h^{3}) \frac{x ^{2}}{2} : \frac{1}{2} x^{2} sec (h^{3})

= \frac{1}{2} x^{2} sec (h^{3})

Add a constant to the solution

= \frac{1}{2} x^{2} sec (h^{3}) + C

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What is the integral of sec(h^3)x ?
The integral of sec(h^3)x is 1/2 x^2sec(h^3)+C