What is the integral of (sec^2(θ))/(sqrt(1+2tan(θ))) ?

The integral of (sec^2(θ))/(sqrt(1+2tan(θ))) is sqrt(1+2tan(θ))+C

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integral of (sec^2(θ))/(sqrt(1+2tan(θ)))

\int \frac{sec ^{2} ( θ )}{1 + 2 tan ( θ )} d θ

1 + 2 tan (θ) + C

Solution steps

\int \frac{sec ^{2} ( θ )}{1 + 2 tan ( θ )} d θ

Apply u-substitution

: \int 1 d u

= \int 1 d u

Integral of a constant:

\int a d x = a x

= 1 \cdot u

Substitute back

u = 1 + 2 tan (θ)

= 1 \cdot 1 + 2 tan (θ)

Simplify

= 1 + 2 tan (θ)

Add a constant to the solution

= 1 + 2 tan (θ) + C

f (x) = x^{4}, at x = 6.87

\int x^{3} + 2 x + 1 d x

f (x) = \frac{2 x ^{2}}{x + 3}

(2 x - 1)^{2}

x \to 0 - lim (18 - x^{2})

What is the integral of (sec^2(θ))/(sqrt(1+2tan(θ))) ?
The integral of (sec^2(θ))/(sqrt(1+2tan(θ))) is sqrt(1+2tan(θ))+C