What is the integral of xsec(2)(x) ?

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

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integral of xsec(2)(x)

\int x sec (2) (x) d x

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

Solution steps

\int x sec (2) x d x

Take the constant out:

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

= sec (2) \cdot \int xx d x

Simplify

xx : x^{2}

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

Apply the Power Rule

: \frac{x ^{3}}{3}

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

Simplify

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

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

Add a constant to the solution

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

x, 0, 2

\int x^{\frac{3}{7}} d x

\frac{0.1}{s + 0.1}

\frac{d}{d x} (x z + x y + y z)

\int_{2}^{3} \frac{x ^{4} + 1}{x ^{5} + 5 x} d x

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