- #1
Cmertin
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I'm having some problems integrating fractions. If you could help me understand it, that would be great.
[tex]\int\frac{2+3sin^{2}x}{5sin^{2}x}[/tex]
[tex]\int(x)dx=\frac{x^{n+1}}{n+1}[/tex]
[tex]\frac{2+3sin^{2}x}{5sin^{2}x}=\frac{1}{5}(\frac{2}{sin^{2}x}+\frac{3sin^{2}x}{sin^{2}x})[/tex]
[tex]=\frac{1}{5}(\frac{2}{sin^{2}x}+\frac{3sin^{2}x}{sin^{2}x})[/tex]
[tex]=\frac{1}{5}(\frac{2}{sin^{2}x}+3)[/tex]
[tex]\frac{1}{5}\int\frac{2}{sin^{2}x}+3 dx=\frac{1}{5}(\frac{-2}{sin(x)cos(x)}+3x)+C[/tex]
This is wrong though because the answer is supposed to be:
[tex]\frac{1}{5}(3x-2cot(x))[/tex]
What did I do wrong?
Homework Statement
[tex]\int\frac{2+3sin^{2}x}{5sin^{2}x}[/tex]
Homework Equations
[tex]\int(x)dx=\frac{x^{n+1}}{n+1}[/tex]
The Attempt at a Solution
[tex]\frac{2+3sin^{2}x}{5sin^{2}x}=\frac{1}{5}(\frac{2}{sin^{2}x}+\frac{3sin^{2}x}{sin^{2}x})[/tex]
[tex]=\frac{1}{5}(\frac{2}{sin^{2}x}+\frac{3sin^{2}x}{sin^{2}x})[/tex]
[tex]=\frac{1}{5}(\frac{2}{sin^{2}x}+3)[/tex]
[tex]\frac{1}{5}\int\frac{2}{sin^{2}x}+3 dx=\frac{1}{5}(\frac{-2}{sin(x)cos(x)}+3x)+C[/tex]
This is wrong though because the answer is supposed to be:
[tex]\frac{1}{5}(3x-2cot(x))[/tex]
What did I do wrong?
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