What is the integral of sqrt(1+(-tan(x))^2) ?

The integral of sqrt(1+(-tan(x))^2) is ln|tan(x)+sec(x)|+C

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integral of sqrt(1+(-tan(x))^2)

\int 1 + (- tan (x))^{2} d x

ln ∣ tan (x) + sec (x) ∣ + C

Solution steps

\int 1 + (- tan (x))^{2} d x

Simplify

1 + (- tan (x))^{2} : sec^{2} (x)

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

sec^{2} (x) = (sec (x)),

assuming

sec (x) \geq 0

= \int sec (x) d x

Use the common integral:

\int sec (x) d x = ln ∣ tan (x) + sec (x) ∣

= ln ∣ tan (x) + sec (x) ∣

Add a constant to the solution

= ln ∣ tan (x) + sec (x) ∣ + C

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x \to 1 lim (\frac{x ^{2}}{1 - x ^{2}})

\frac{d}{d t} (6 t^{3})

What is the integral of sqrt(1+(-tan(x))^2) ?
The integral of sqrt(1+(-tan(x))^2) is ln|tan(x)+sec(x)|+C