Question

instigation of sin 5x cos 2x dx​

Answer 1

Step-by-step explanation:

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Answer 2

Given ,

The function is Sin(5x)Cos(2x)

Integrating wrt to x , we get

$\tt \implies \int{Sin(5x)Cos(2x)} \: \: dx$

Multiplying numerator and denominator by 2 , we get

$\tt \implies \int{ \frac{2Sin(5x)Cos(2x)}{2} } \: \: dx$

$\tt \implies \frac{1}{2} \int{2Sin(5x)Cos(2x)} \: \: dx$

$\tt \implies \frac{1}{2} \int{Sin(7x) + Cos(3x)} \: \: dx$

$\tt \implies \frac{1}{2} \{ \int{Sin(7x) \: \: dx + \int Sin(3x)} \: \: dx \}$

$\tt \implies \frac{1}{2} \{ - \frac{ Cos(7x)}{7} </p><p>- \frac{Cos(3x)}{3} \} + c$

$\tt \implies - \frac{ Cos(7x)}{14} - \frac{Cos(3x)}{6} + c$

Remmember :

$\tt \mapsto 2Sin(x)Cos(y) = Sin(x + y) +Sin(x - y)$

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