CBSE Class 12-science Answered
integration tan²xsec?xdx
Asked by diptiranigupta1981 | 02 Oct, 2023, 18:33: PM
![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](https://images.topperlearning.com/topper/tinymce/cache/471af767b4e54d8a0fe15bebc6e5bf8a.png)
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](https://images.topperlearning.com/topper/tinymce/cache/825f09a0bc2d2516c0934f7530d8fdc3.png)
![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](https://images.topperlearning.com/topper/tinymce/cache/825f09a0bc2d2516c0934f7530d8fdc3.png)
![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](https://images.topperlearning.com/topper/tinymce/cache/8d6869389c71d6f2e6f556a7c64878ea.png)
![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](https://images.topperlearning.com/topper/tinymce/cache/78413d94ea05fb487d2c71cc2619193d.png)
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](https://images.topperlearning.com/topper/tinymce/cache/7fa2c0c718f57114583839d15de40a7f.png)
Answered by Thiyagarajan K | 02 Oct, 2023, 21:59: PM
Concept Videos
CBSE 12-science - Maths
Asked by aalavarshitha2005 | 21 Jan, 2024, 17:28: PM
CBSE 12-science - Maths
Asked by atharvaparkar04 | 17 Dec, 2023, 12:59: PM
CBSE 12-science - Maths
Asked by shashinayaka032 | 05 Dec, 2023, 12:46: PM
CBSE 12-science - Maths
Asked by manasvichandel49 | 19 Oct, 2023, 08:53: AM
CBSE 12-science - Maths
Asked by diptiranigupta1981 | 02 Oct, 2023, 18:33: PM
CBSE 12-science - Maths
Asked by sdmbotch1123 | 30 Sep, 2023, 22:54: PM
CBSE 12-science - Maths
Asked by sdmbotch1123 | 16 Jan, 2023, 20:18: PM
CBSE 12-science - Maths
Asked by devilkano80 | 07 Jul, 2022, 13:45: PM