Example 15 - Find (3 sin - 2) cos / 5 - cos2 - 4 sin - Integration by partial fraction - Type 2

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  1. Class 12
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Example 15 Find 3 sin 2 cos 5 cos 2 4 sin Let = sin Differentiating w.r.t. = cos cos = Now we can write 3 sin 2 cos 5 cos 2 4 sin = 3 sin 2 cos 5 sin 2 1 4 sin = 3 2 cos 5 1 + 2 4 cos = 3 2 4 + 2 4 = 3 2 2 + 2 2 2.2 = 3 2 2 2 We can write integrand 3 2 2 2 = 2 + 2 2 3 2 2 2 = 2 + 2 2 By Cancelling denominator 3 2 = 2 + 3 2 = 2 + Hence we can write it as 3 2 2 2 = 3 2 + 4 2 2 Now, our equation becomes 3 2 2 2 = 3 2 + 4 2 2 =3 log 2 +4 2 1 1 + =3 log 2 4 1 2 + Substituting back the value of t =3 log sin 2 4 sin 2 + = + +

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.