Final answer to the problem
$x\sin\left(y\right)+y\cos\left(x\right)+C_0$
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Step-by-step Solution
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- Integrate by partial fractions
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- Weierstrass Substitution
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- Product of Binomials with Common Term
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1
Expand the integral $\int\left(\sin\left(y\right)-y\sin\left(x\right)\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately
$\int\sin\left(y\right)dx+\int-y\sin\left(x\right)dx$
Learn how to solve integrals of polynomial functions problems step by step online. Find the integral int(sin(y)-ysin(x))dx. Expand the integral \int\left(\sin\left(y\right)-y\sin\left(x\right)\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\sin\left(y\right)dx results in: x\sin\left(y\right). The integral \int-y\sin\left(x\right)dx results in: y\cos\left(x\right). Gather the results of all integrals.
Final answer to the problem
$x\sin\left(y\right)+y\cos\left(x\right)+C_0$
