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- Integrate by partial fractions
- Integrate by substitution
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- Integrate using tabular integration
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- Weierstrass Substitution
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- Integrate using basic integrals
- Product of Binomials with Common Term
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Applying the cosecant identity: $\displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}$
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$\int\cos\left(2x\right)\left(\sin\left(2x\right)^2+7\csc\left(2x\right)\right)^2dx$
Learn how to solve problems step by step online. Solve the trigonometric integral int(cos(2x)(sin(2x)^2+7/sin(2x))^2)dx. Applying the cosecant identity: \displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}. Rewrite the integrand \cos\left(2x\right)\left(\sin\left(2x\right)^2+7\csc\left(2x\right)\right)^2 in expanded form. Expand the integral \int\left(\sin\left(2x\right)^{4}\cos\left(2x\right)+14\sin\left(2x\right)\cos\left(2x\right)+49\csc\left(2x\right)^{2}\cos\left(2x\right)\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. Simplify the expression.
