Final answer to the problem
$\frac{\sec\left(x\right)^{2}+\tan\left(x\right)\sec\left(x\right)}{2}+\frac{1}{2}\ln\left|\sec\left(x\right)+\tan\left(x\right)\right|-\tan\left(x\right)\sec\left(x\right)+C_0$
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Step-by-step Solution
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- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
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1
Reduce $\frac{1}{\cos\left(x\right)+\cot\left(x\right)}$ by applying trigonometric identities
$\int\frac{\tan\left(x\right)}{1+\sin\left(x\right)}dx$
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$\int\frac{\tan\left(x\right)}{1+\sin\left(x\right)}dx$
Learn how to solve problems step by step online. Solve the trigonometric integral int(1/(cos(x)+cot(x)))dx. Reduce \frac{1}{\cos\left(x\right)+\cot\left(x\right)} by applying trigonometric identities. Rewrite the trigonometric expression \frac{\tan\left(x\right)}{1+\sin\left(x\right)} inside the integral. Expand the fraction \frac{\sin\left(x\right)-\sin\left(x\right)^2}{\cos\left(x\right)^{3}} into 2 simpler fractions with common denominator \cos\left(x\right)^{3}. Simplify the expression.
Final answer to the problem
$\frac{\sec\left(x\right)^{2}+\tan\left(x\right)\sec\left(x\right)}{2}+\frac{1}{2}\ln\left|\sec\left(x\right)+\tan\left(x\right)\right|-\tan\left(x\right)\sec\left(x\right)+C_0$
