Integral Calculus> evaluate ∫ (sin^3(x) – cos^3(x)) / sin^2(...

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

taniska , 10 Years ago

Grade 12

1 Answers

Jitender Singh

Last Activity: 10 Years ago

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

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