What is the integral of sec(1/2)xtan(1/2)x ?

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

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integral of sec(1/2)xtan(1/2)x

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

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

Solution steps

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

Take the constant out:

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

= sec (\frac{1}{2}) tan (\frac{1}{2}) \cdot \int xx d x

Simplify

xx : x^{2}

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

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

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

f (x) = 3 x + 3

\frac{d ^{2}}{d x ^{2}} (k x)

n = 1 \sum \infty \frac{x ^{n}}{n \cdot 5 n}

\frac{d}{d x} ((x^{3} - 16 x)^{10})

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