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

Rewrite using trig identities

= \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

g (x) = 6 - x

\frac{1}{1 - x}, 0, 1

\int 3 x^{5} d x

n = 9 \sum \infty e^{3 - 4 n}

y = cos^{4} (x) - sin^{4} (x)

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