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

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

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

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

2 1 + tan (x) + C

Solution steps

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

Apply u-substitution

: \int 2 d u

= \int 2 d u

Integral of a constant:

\int a d x = a x

= 2 u

Substitute back

u = 1 + tan (x)

= 2 1 + tan (x)

Add a constant to the solution

= 2 1 + tan (x) + C

\frac{( e ^{x} + e ^{- x} ) d y}{d x} = y^{2}

\frac{d}{d x} (\frac{1}{x ^{2} - 9})

\int 3 x e^{4 x} d x

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

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