Integral Calculus> evaluate ∫(5cos^3(x) + 6sin^3(x)) / 2sin^...

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

taniska , 11 Years ago

Grade 12

1 Answers

Jitender Singh

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

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