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

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

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integral of 1/(1+cos(2t))

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

\frac{1}{2} tan (t) + C

Solution steps

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

Rewrite using trig identities

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int \frac{1}{cos ^{2} ( t )} d t

Use the common integral:

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

= \frac{1}{2} tan (t)

Add a constant to the solution

= \frac{1}{2} tan (t) + C

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