Question

integration of1/a+btanx

Answer 1

hayy mate here your answer ✔️ ✔️
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One of the ways:

1/[a + b*tan(x)] = cos(x)/[a*cos(x) + b * sin(x)]

let

a/√(a2 + b2) = sin(Φ) and

b/√(a2 + b2) = cos(Φ)

then

1/[a + b*tan(x)] = 1/√(a2 + b2) * {cos(x) / [sin(Φ)*cos(x) + cos(Φ) * sin(x)]} = 1/√(a2 + b2) * {cos(x) / sin(Φ + x)}

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❤️⭐I hope you mark as brainlist answer⭐❤️✨✨✨