Find the integral 1/4int(2sec(z))dz

 Exercise

$\frac{1}{4}\int2seczdz$

 

The integral of a function times a constant ($2$) is equal to the constant times the integral of the function

$2\left(\frac{1}{4}\right)\int\sec\left(z\right)dz$

 

Multiply the fraction and term in $2\left(\frac{1}{4}\right)\int\sec\left(z\right)dz$

$\frac{1}{2}\int\sec\left(z\right)dz$

 

The integral of the secant function is given by the following formula, $\displaystyle\int\sec(x)dx=\ln\left|\sec(x)+\tan(x)\right|$

$\frac{1}{2}\ln\left|\sec\left(z\right)+\tan\left(z\right)\right|$

 

As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$

$\frac{1}{2}\ln\left|\sec\left(z\right)+\tan\left(z\right)\right|+C_0$

$\frac{1}{2}\ln\left|\sec\left(z\right)+\tan\left(z\right)\right|+C_0$

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