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प्रश्न
Integrate the following with respect to x:
`(x + 4)^5 + 5/(2 - 5x)^4 - "cosec"^2 (3x - 1)`
उत्तर
`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"`
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