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

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

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

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

2 1 + tan (x) + C

Solution steps

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

Rewrite using trig identities

= \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{\partial}{\partial x} (\frac{9 x}{y})

y = x x, (9, 27)

\frac{d}{d n} (5^{n})

x \to 4 lim (\frac{8}{x})

\int \frac{1}{x ^{2} + 2 x + 5} d x

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