Integral of \( \displaystyle \frac{\sin{\left(x \right)}}{\cos^{2}{\left(x \right)}} \)

Problem 4.181 · medium

1. \[ \int \frac{\sin{\left(x \right)}}{\cos^{2}{\left(x \right)}}\, dx \]
   integral algebraStart with the integral of the given function. Rewrite the fraction as a product.✓ Proved
2. \[ = \int \sin{\left(x \right)} \sec^{2}{\left(x \right)}\, dx \]
   rewriteUse the identity 1/cos(x)**2 = sec(x)**2.✓ Proved
3. \[ = \int \tan{\left(x \right)} \sec{\left(x \right)}\, dx \]
   rewriteUse the identity sin(x)/cos(x) = tan(x).✓ Proved
4. \[ = \sec{\left(x \right)} \]
   antiderivativeThe antiderivative of sec(x)tan(x) is sec(x).✓ Proved