What is the integral of 1/((cosh(x))^2) ?

The integral of 1/((cosh(x))^2) is tanh(x)+C

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integral of 1/((cosh(x))^2)

\int \frac{1}{( cosh ( x ) ) ^{2}} d x

tanh (x) + C

Solution steps

\int \frac{1}{( cosh ( x ) ) ^{2}} d x

Use the Hyperbolic identity:

\frac{1}{cosh ( x )} = sech (x)

= \int sech^{2} (x) d x

Use the common integral:

\int sech^{2} (x) d x = tanh (x)

= tanh (x)

Add a constant to the solution

= tanh (x) + C

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What is the integral of 1/((cosh(x))^2) ?
The integral of 1/((cosh(x))^2) is tanh(x)+C