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Prove that , int a^(x) dx = (a^(x))/(lo...

Prove that , ` int a^(x) dx = (a^(x))/(log_(e)a)+ c , ` where ` a gt 0 ` . Does the formula hold for a = 1 ?

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CHHAYA PUBLICATION-IDENFINITE INTEGRAL -Very short Answer Type Questions
  1. Prove that , int a^(x) dx = (a^(x))/(log(e)a)+ c , where a gt 0 ....

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  2. Prove by using definition of indefinite integral : int sin mx dx...

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  3. Prove by using definition of indefinite integral : int cos mx dx ...

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

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

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

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

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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 = (a...

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

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

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

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

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

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

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

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

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

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

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

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