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Prove by using definition of indefinite ...

Prove by using definition of indefinite integral :
` int "cosec"^(2) mx dx = - (cot mx)/m + c`
where ` m != 0 ` is a constant independent of x and c is an arbitrary constant .

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CHHAYA PUBLICATION-IDENFINITE INTEGRAL -Very short Answer Type Questions
  1. Prove by using definition of indefinite integral : int cos mx dx ...

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  2. Prove by using definition of indefinite integral : int sec^(2) mx...

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  3. Prove by using definition of indefinite integral : int "cosec"^(2...

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  4. Prove by using definition of indefinite integral : int sec mx tan...

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  5. Prove by using definition of indefinite integral : int " cosec" m...

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  6. Using the definition of integration find y in terms of x : (dy)/(dx...

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  7. Using the definition of integration find y in terms of x : dy = (a...

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  8. Using the definition of integration find y in terms of x : (dy)/(dx...

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  9. Using the definition of integration find y in terms of x : (dy)/(d...

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  10. Integrate each of the following functions w.r.t . X : x^(2/3)

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  11. Integrate each of the following functions w.r.t . X : 2/(root4(x^(...

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  12. Integrate each of the following functions w.r.t . X : x^(4) - 2x^(...

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  13. Integrate each of the following functions w.r.t . X : (x - 2/x)^(3)

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  14. Integrate each of the following functions w.r.t . X : (x+3)(x^(2)-...

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  15. Integrate each of the following functions w.r.t . X : 1/(sqrt(x)) (...

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  16. Evaluate : int e^(3 log x)dx

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  17. Evaluate : int ((e^(5x)-2e^(3x)+3))/(e^(x)) dx

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  18. Evaluate : int (e^(5x)+e^(3x))/(e^(x)+e^(-x)) dx

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  19. Evaluate : int (e^(2logx)- 2e^(-3 log x) ) dx

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  20. Evaluate : int e^(-4x) dx

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