Grade 12Integral Calculus

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

taniska

11 Years agoGrade 12

1 Answer

Jitender Singh

11 Years ago

Ans:
Hello Student,
Please find answer to your question below

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