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evaluate ∫(5cos^3(x) + 6sin^3(x)) / 2sin^2(x) cos^2(x) dx

evaluate
∫(5cos^3(x) + 6sin^3(x)) / 2sin^2(x) cos^2(x) dx

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
Hello Student,
Please find answer to your question below

I = \int \frac{5cos^3x+6sin^3x}{2sin^2xcos^2x}dx
I = \int (\frac{5cosx}{2sin^2x}+\frac{3sinx}{cos^{2}x})dx
I = \int \frac{5cosx}{2sin^2x}dx+\int \frac{3sinx}{cos^{2}x}dx
I_{1} = \int \frac{5cosx}{2sin^2x}dx
sinx = t
cosxdx = dt
I_{1} = \int \frac{5}{2t^2}dt
I_{1} = \frac{-5}{2t} + c
I_{1} = \frac{-5}{2sinx} + c
I_{2} = \int \frac{3sinx}{cos^{2}x}dx
cosx = t
-sinxdx = dt
I_{2} = \int \frac{-3}{t^{2}}dt
I_{2} = \frac{3}{t} + d
I_{2} = \frac{3}{cosx} + d
I = \frac{-5}{2sinx} + \frac{3}{cosx} + c + d
I = \frac{-5}{2sinx} + \frac{3}{cosx} + e

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