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CBSE Class 12-science Answered

1.   Solveƒ [x3sin(tan-1x4)/(1+x8)]dx

Asked by pramodtalukdar | 16 Sep, 2016, 06:41: AM
answered-by-expert Expert Answer
I equals integral fraction numerator x cubed sin open parentheses tan to the power of negative 1 end exponent x to the power of 4 close parentheses over denominator 1 plus x to the power of 8 end fraction d x
A p p l y space i n t e g r a l space s u b s t i t u t i o n space integral f open parentheses g left parenthesis x right parenthesis close parentheses. g apostrophe left parenthesis x right parenthesis d x space equals integral f left parenthesis u right parenthesis d u space
u space equals space g left parenthesis x right parenthesis comma space u space equals x to the power of 4 space space d u space equals space 4 x cubed d x space

I equals integral fraction numerator u over denominator 4 open parentheses u squared plus 1 close parentheses square root of u squared plus 1 end root end fraction d u
I equals 1 fourth integral u over open parentheses u squared plus 1 close parentheses to the power of begin display style bevelled 3 over 2 end style end exponent d u

P u t space v space equals space open parentheses u squared plus 1 close parentheses

I equals 1 over 8 integral 1 over v to the power of begin display style bevelled 3 over 2 end style end exponent d u

I space equals space 1 over 8 cross times fraction numerator v to the power of begin display style bevelled fraction numerator negative 1 over denominator 2 end fraction end style end exponent over denominator negative begin display style 1 half end style end fraction

I space equals negative space fraction numerator 1 over denominator 4 square root of x to the power of 8 plus 1 end root end fraction plus C
Answered by Vijaykumar Wani | 16 Sep, 2016, 07:03: PM
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