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evaluate ∫ (sin^3(x) – cos^3(x)) / sin^2(x) cos^2(x) dx

evaluate
∫ (sin^3(x) – cos^3(x)) / sin^2(x) cos^2(x) dx

Grade:12

1 Answers

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

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

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