Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Integrate using basic integrals
- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using trigonometric identities
- Product of Binomials with Common Term
- FOIL Method
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We can solve the integral $\int\frac{1}{2\sin\left(t\right)+\cos\left(t\right)+5}dt$ by applying the method Weierstrass substitution (also known as tangent half-angle substitution) which converts an integral of trigonometric functions into a rational function of $t$ by setting the substitution
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$t=\tan\left(\frac{t}{2}\right)$
Learn how to solve differential equations problems step by step online. Solve the trigonometric integral int(1/(2sin(t)+cos(t)+5))dt. We can solve the integral \int\frac{1}{2\sin\left(t\right)+\cos\left(t\right)+5}dt by applying the method Weierstrass substitution (also known as tangent half-angle substitution) which converts an integral of trigonometric functions into a rational function of t by setting the substitution. Hence. Substituting in the original integral we get. Simplifying.