Calculus Quiz 5-(1)

Evaluate the integrals

$$\int \frac{{\mathrm{sech}}^2 x}{2+\tanh x} dx$$

Sol)

$2+\tanh x=t$로 치환하면, ${\mathrm{sech}}^2 x \, dx=dt$

$$\int \frac{{\mathrm{sech}}^2 x}{2+\tanh x} dx = \int\frac{1}{t} dt = \ln t +C$$

$$ \therefore \int \frac{{\mathrm{sech}}^2 x}{2+\tanh x} dx = \ln{\left(\tanh x +2 \right)} + C$$