CBSE Class 12-science Answered

integration tan²xsec⁴xdx

Asked by diptiranigupta1981 | 02 Oct, 2023, 06:33: PM

Expert Answer

begin mathsize 14px style I space equals space integral tan squared x space space s e c to the power of 4 x space d x space end style

Let u = tan(x) ; du = sec²(x) dx

also ,

begin mathsize 14px style s e c to the power of 4 x space d x space equals space s e c to the power of 2 space end exponent x space space s e c squared x space space d x space equals space left parenthesis space 1 space plus space tan squared x space right parenthesis space s e c squared x space d x end style

begin mathsize 14px style s e c to the power of 4 x space d x space equals space left parenthesis space 1 space plus space u squared space right parenthesis space d u end style

begin mathsize 14px style I space equals space integral tan squared x space space s e c to the power of 4 x space d x space equals space integral space u squared space left parenthesis 1 plus u squared space right parenthesis space d u space equals space integral space left parenthesis space u to the power of 2 space end exponent space plus space u to the power of 4 space right parenthesis space d u end style

Hence we get

begin mathsize 14px style I space equals space u cubed over 3 space plus space u to the power of 5 over 5 space plus space C space equals space fraction numerator tan cubed x over denominator 3 end fraction space plus space fraction numerator tan to the power of 5 x over denominator 5 end fraction plus C end style

Answered by Thiyagarajan K | 02 Oct, 2023, 09:59: PM

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