What is the integral of sec(x+pi/2)tan(x+pi/2) ?

The integral of sec(x+pi/2)tan(x+pi/2) is sec(x+pi/2)+C

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integral of sec(x+pi/2)tan(x+pi/2)

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

sec (x + \frac{π}{2}) + C

Solution steps

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

Apply u-substitution

: \int sec (u) tan (u) d u

= \int sec (u) tan (u) d u

Apply u-substitution

: \int 1 d v

= \int 1 d v

Integral of a constant:

\int a d x = a x

= 1 \cdot v

Substitute back

= 1 \cdot sec (x + \frac{π}{2})

Simplify

= sec (x + \frac{π}{2})

Add a constant to the solution

= sec (x + \frac{π}{2}) + C

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What is the integral of sec(x+pi/2)tan(x+pi/2) ?
The integral of sec(x+pi/2)tan(x+pi/2) is sec(x+pi/2)+C