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evaluate ∫ { 3 sin x – 4 cos x + 5/cos^2(x) – 6/sin^2(x) + tan^2(x) – cot^2(x)} dx

evaluate
∫ { 3 sin x – 4 cos x + 5/cos^2(x) – 6/sin^2(x) + tan^2(x) – cot^2(x)} dx

Grade:12

1 Answers

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

I = \int (3sinx-4cosx+\frac{5}{cos^{2}x}-\frac{6}{sin^{2}x}+tan^{2}x-cot^{2}x)dx
I = \int (3sinx-4cosx+5sec^{2}x-6cosec^{2}x+tan^{2}x-cot^{2}x)dx
I = \int (3sinx-4cosx+5sec^{2}x-6cosec^{2}x+sec^{2}x-1-cosec^{2}x+1)dxI = \int (3sinx-4cosx+6sec^{2}x-7cosec^{2}x)dx
I = -3cosx-4sinx+6tanx+7cotx+c

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