Question #136205
\int \left(\frac{sin\left(x+a\right)}{m}+\frac{cos\left(x+b\right)}{n}\right)dx
1
Expert's answer
2020-10-05T17:07:40-0400

\int \left(\frac{sin\left(x+a\right)}{m}+\frac{cos\left(x+b\right)}{n}\right)dx(sin(x+a)m+cos(x+b)n)dx=(sin(x+a)m)dx+(cos(x+b)n)dx=\int \left(\frac{sin\left(x+a\right)}{m}+\frac{cos\left(x+b\right)}{n}\right)dx=\int \left(\frac{sin\left(x+a\right)}{m}\right)dx+\int \left(\frac{cos\left(x+b\right)}{n}\right)dx=

cos(x+a)m+sin(x+b)n+C-\frac{cos\left(x+a\right)}{m}+\frac{sin\left(x+b\right)}{n}+C

Answer: sin(x+b)ncos(x+a)m+C\frac{sin\left(x+b\right)}{n}-\frac{cos\left(x+a\right)}{m}+C


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