Final answer to the problem
Step-by-step Solution
Specify the solving method
Rewrite the trigonometric expression $\frac{1}{1-\sin\left(x\right)}$ inside the integral
Learn how to solve integral calculus problems step by step online.
$\int\frac{1+\sin\left(x\right)}{1-\sin\left(x\right)^2}dx$
Learn how to solve integral calculus problems step by step online. Solve the trigonometric integral int(1/(1-sin(x)))dx. Rewrite the trigonometric expression \frac{1}{1-\sin\left(x\right)} inside the integral. Applying the trigonometric identity: 1-\sin\left(\theta \right)^2 = \cos\left(\theta \right)^2. Expand the fraction \frac{1+\sin\left(x\right)}{\cos\left(x\right)^2} into 2 simpler fractions with common denominator \cos\left(x\right)^2. Expand the integral \int\left(\frac{1}{\cos\left(x\right)^2}+\frac{\sin\left(x\right)}{\cos\left(x\right)^2}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately.