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

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

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

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

2 1 + tan (t) + C

Solution steps

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

Rewrite using trig identities

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

Apply u-substitution

= \int 2 d u

Integral of a constant:

\int a d x = a x

= 2 u

Substitute back

u = 1 + tan (t)

= 2 1 + tan (t)

Add a constant to the solution

= 2 1 + tan (t) + C

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