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

The integral of xsec^2(x/2) is 2xtan(x/2)+4ln|cos(x/2)|+C

Popular >

integral of xsec^2(x/2)

\int x sec^{2} (\frac{x}{2}) d x

2 x tan (\frac{x}{2}) + 4 ln cos (\frac{x}{2}) + C

Solution steps

\int x sec^{2} (\frac{x}{2}) d x

Apply Integration By Parts

: 2 x tan (\frac{x}{2}) - \int 2 tan (\frac{x}{2}) d x

= 2 x tan (\frac{x}{2}) - \int 2 tan (\frac{x}{2}) d x

\int 2 tan (\frac{x}{2}) d x = - 4 ln cos (\frac{x}{2})

= 2 x tan (\frac{x}{2}) - (- 4 ln cos (\frac{x}{2}))

Simplify

= 2 x tan (\frac{x}{2}) + 4 ln cos (\frac{x}{2})

Add a constant to the solution

= 2 x tan (\frac{x}{2}) + 4 ln cos (\frac{x}{2}) + C

\int \frac{sin ( ln ( x ) )}{2 x} d x

\int \frac{2 x - 1}{4 x - 4 x ^{2}} d x

\int \frac{ln ^{2} ( x ) + ln ( x )}{x ^{2}} d x

\int \frac{u ^{2}}{1 - u ^{2}} d u

\int \frac{16}{1 + 4 x ^{2}} d x

What is the integral of xsec^2(x/2) ?
The integral of xsec^2(x/2) is 2xtan(x/2)+4ln|cos(x/2)|+C