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CBSE Class 12-science Answered

Please solve it step by step
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Asked by pro8mk | 19 May, 2019, 09:11: AM
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I equals integral fraction numerator sin x space e to the power of cos x end exponent minus left parenthesis sin x plus cos x right parenthesis e to the power of sin x plus cos x end exponent over denominator e to the power of 2 sin x end exponent minus 2 e to the power of sin x end exponent plus 1 end fraction d x equals integral fraction numerator sin x space e to the power of cos x end exponent minus sin x space e to the power of sin x plus cos x end exponent plus cos x space e to the power of sin x plus cos x end exponent over denominator left parenthesis e to the power of sin x end exponent minus 1 right parenthesis squared end fraction d x equals integral negative e to the power of cos x end exponent fraction numerator sin x left parenthesis e to the power of sin x end exponent minus 1 right parenthesis plus cos x space e to the power of sin x end exponent over denominator left parenthesis e to the power of sin x end exponent minus 1 right parenthesis squared end fraction d x equals integral fraction numerator negative e to the power of cos x end exponent sin x over denominator left parenthesis e to the power of sin x end exponent minus 1 right parenthesis end fraction d x minus integral fraction numerator cos x space e to the power of sin x end exponent e to the power of cos x end exponent over denominator left parenthesis e to the power of sin x end exponent minus 1 right parenthesis squared end fraction d x L e t space e to the power of sin x end exponent minus 1 equals t space rightwards double arrow space e to the power of sin x end exponent space cos x space d x equals d t A n d space p u t space e to the power of cos x end exponent equals u space rightwards double arrow space space minus e to the power of cos x end exponent space sin x space d x equals d u rightwards double arrow I equals integral fraction numerator d u over denominator t end fraction minus fraction numerator u d t over denominator t squared end fraction rightwards double arrow I equals integral fraction numerator t d u minus u d t over denominator t squared end fraction rightwards double arrow I equals integral fraction numerator d over denominator d t end fraction open parentheses u over t close parentheses rightwards double arrow I equals u over t plus c equals fraction numerator e to the power of cos x end exponent over denominator space e to the power of sin x end exponent minus 1 end fraction plus c H e n c e comma space I equals fraction numerator e to the power of cos x end exponent over denominator space e to the power of sin x end exponent minus 1 end fraction plus c
Answered by Renu Varma | 20 May, 2019, 11:28: AM

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