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Given inte^x\ (tanx+1)secx\ dx=e^xf(x)+c...

Given `inte^x\ (tanx+1)secx\ dx=e^xf(x)+c` write `f(x)` satisfying the above.

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The correct Answer is:
`secx`.
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OSWAAL PUBLICATION-INTEGRALS-DEFINITE INTEGRALS (LONG TYPE ANSWER TYPE QUESTIONS - III)
  1. Given inte^x\ (tanx+1)secx\ dx=e^xf(x)+c write f(x) satisfying the ab...

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  2. Prove that int(0)^(2a) f(x) dx = 2int(0)^(a) f(x) dx when f(2a -x) = f...

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  3. Prove that int(-a)^(a) dx = {(2int(0)^(a) f(x) dx, if f(x) "is even"),...

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  4. Evaluate int0pi/2(sin^4x)/(sin^4x+cos^4x)""dx

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  5. int0^1log(1+x)/(1+x^2)dx

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  6. Prove that int(a)^(b)f(x)dx=int(a)^(b)f(a+b-x)dx and hence evaluate in...

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  7. Prove that int(0)^(a)(x)dx = int(0)^(a) f(a-x)dx and hence evaluate in...

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  8. Evaluate the following integrals: (1-35) int(-1)^1|xcospix|dx

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  9. int0^(pi/2)x^2sinx dx

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  10. Evaluate: int0^(pi/4)(sinx+cosx)/(9+16sin2x)dx

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  11. Show that : int0^(pi/2)(sin^2x)/(sinx+cosx)dx=1/(sqrt(2))log(sqrt(2)+1...

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  12. Evaluate the definite integrals intpi/6pi/3(sinx+cosx)/(sqrt(sin2x)...

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  13. Evaluate : int(0)^(pi)(4xsinx)/(1+cos^(2)x)dx.

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  14. Evaluate : int0^(pi/4)log(1+tanx)dxdot

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  15. int0^(pi/2)(sin2theta)/(sin^4theta+cos^4theta) d theta

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  16. Evaluate: int0^4(|x|+|x-2|+|x-4|)\ dx

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  17. int2^5(|x-2|+|x-3|+|x-5|)dx

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  18. Evaluate: int0^(2pi)1/(1+e^(sinx))dx

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  19. Evaluate int(0)^(pi)(xsinx)/((1+cos^(2)x))dx.

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  20. Evaluate : int(-1)^2|x^3-x|\ dx

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  21. Evaluate: int(pi//4)^(pi//2)cos2xlogsinxdx

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