Tamil Nadu Board of Secondary EducationHSC Arts Class 11

Integrate the following with respect to x: cosec(x+4)5+5(2-5x)4-cosec2(3x-1) - Mathematics

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Sum

Integrate the following with respect to x:

`(x + 4)^5 + 5/(2 - 5x)^4 - "cosec"^2 (3x - 1)`

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Solution

`int [(x + 4)^5 + 5/(2 - 5x)^4 - "cosec"^2 (3x - 1)] "d"x`

= `int (x + 4)^5 "d"x + 5 int 1/(2 - 5x)^4  "d"x - int  "cosec"^2(3x - 1)  "d"x`

= `(x + 4)^6/6 + (- 5)/(- 5 xx 3(2 - 5x)^3) + (cot(3x - 1))/3 + "c"`

= `(x + 4)^6/6 + 1/(3(2 - 5x)^3) + (cot(3x - 1))/3 + "c"`

Concept: Properties of Integrals
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Chapter 11: Integral Calculus - Exercise 11.3 [Page 192]

APPEARS IN

Tamil Nadu Board Samacheer Kalvi Class 11th Mathematics Volume 1 and 2 Answers Guide
Chapter 11 Integral Calculus
Exercise 11.3 | Q 1 | Page 192
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