What is the integral of sec^2(x+2) ?

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

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integral of sec^2(x+2)

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

tan (x + 2) + C

Solution steps

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

Apply u-substitution

: \int sec^{2} (u) d u

= \int sec^{2} (u) d u

Use the common integral:

\int sec^{2} (u) d u = tan (u)

= tan (u)

Substitute back

u = x + 2

= tan (x + 2)

Add a constant to the solution

= tan (x + 2) + C

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