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Grade 12Integral Calculus

evaluate the following integral
∫ (2 cos x – 3 sin x) / (6 cos x + 4 sin x) dx

taniska

11 Years agoGrade 12

1 Answer

Jitender Singh

11 Years ago

Ans:
Hello student,
Please find the answer to your question below

$I = \int \frac{2cosx-3sinx}{6cosx+4sinx}dx$
$6cosx + 4sinx = t$
$(-6sinx+4cosx)dx = dt$
$2(-3sinx+2cosx)dx = dt$
$I = \int \frac{dt}{2t}$
$I = \frac{logt}{2} + c$
$I = \frac{log(4sinx+6cosx)}{2} + c$

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