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in Integration by (48.0k points)

Integrate the following :

(a) \(\int e^x(\frac{1 - sinx}{1 - cosx})dx\)

(b) \(\int e^x [loga + \frac{1}{x^2}]dx\)

2 Answers

+1 vote
by (46.3k points)
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Best answer

(a) \(\int e^x(\frac{1 - sinx}{1 - cosx})dx\)

(b) \(\int e^x [loga + \frac{1}{x^2}]dx\)

+1 vote
by (1.7k points)

(A) This is the first answerSlide10.JPG

Slide11.JPGSlide12.JPG

(B)

integral e to the power of x left parenthesis log space x plus 1 over x squared right parenthesis d x integral e to the power of x left parenthesis log x plus 1 over x minus 1 over x plus 1 over x squared right parenthesis d x integral e to the power of x left parenthesis log x space plus 1 over x right parenthesis d x space space plus integral space e to the power of x left parenthesis negative 1 over x plus 1 over x squared right parenthesis d x  w e space h a v e space integral e to the power of space x end exponent left parenthesis f left parenthesis x right parenthesis plus f apostrophe left parenthesis x right parenthesis right parenthesis d x equals space e to the power of x f left parenthesis x right parenthesis plus C integral e to the power of x left parenthesis log x space plus 1 over x right parenthesis d x space space plus integral space e to the power of x left parenthesis negative 1 over x plus 1 over x squared right parenthesis d x equals equals e to the power of x left parenthesis log x right parenthesis space plus e to the power of space x end exponent left parenthesis negative 1 over x right parenthesis space plus c

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