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Evaluate: int(secx)/(secx+tanx)dxdot...

Evaluate: `int(secx)/(secx+tanx)dxdot`

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To evaluate the integral \[ I = \int \frac{\sec x}{\sec x + \tan x} \, dx, \] we can use a substitution method and some algebraic manipulation. ...
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RD SHARMA ENGLISH-INDEFINITE INTEGRALS-All Questions
  1. Evaluate: 1/(1+cosx)\ dx

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  2. Evaluate: int(sinx)/(1+sinx)\ dx

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  3. Evaluate: int(secx)/(secx+tanx)dxdot

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  4. Evaluate: int(s in^6\ x+cos^6\ x)/(s in^2\ x\ cos^2\ x)

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  5. Evaluate: int(1+cos4x)/(cotx-tanx)\ dx

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  6. int(1)/(tanx+cotx+secx+"cosec "x)dx is equal to

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  7. Evaluate: (i) intsin^(-1)(cosx)\ dx ,\ \ 0lt=xlt=pi (ii) inttan^(-1){...

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  8. Evaluate int tan^(-1)(secx+tanx)dx,-pi//2ltxlt pi//2

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  9. Evaluate: inttan^(-1){sqrt(((1-sinx)/(1+sinx)))}\ dx ,\ -pi//2<x<pi//2

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  10. Evaluate: inte^(xlogea)+e^(alogex)+e^(alogea)\ dx

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  11. Evaluate: int(x/m+m/x+x^m+m^x)\ dx

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  12. Evaluate: (i) int(2^x+3^x)/(5^x)\ dx (ii) int((a^x+b^x)^2)/(a^x\ b\ ^x...

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  13. Evaluate: (i) int(x^4+x^2+1)\ d(x^2) (ii) intsin(e^x)d(e^x)

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  14. If f^(prime)(x)=3x^2-2/(x^3) and f(1)=0 , find f(x) .

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  15. Evaluate the following: int(3xsqrt(x)+4sqrt(x)+5)\ dx (ii) int(2^x...

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  16. Evaluate: (i) int{sqrt(x)(a x^2+b x+c)}\ dx (ii) int(2-3x)(3+2x)(1-2x...

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  17. Evaluate: (i)int(m/x+x/m+m^x+x^m+m x)\ dx (ii) int(sqrt(x)-1/(sqrt(x))...

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  18. Evaluate: (i) int((1+x)^3)/(sqrt(x))\ dx (ii) int{x^2+e^(logx)+(e/2)^x...

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  19. Evaluate: (i) int(x^e+e^x+e^e)\ dx (ii) intsqrt(x)(x^3-2/x)\ dx

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  20. Evaluate: (i) int(x^(-1//3)+sqrt(x)+2)/(x3)\ dx (ii) int((1+sqrt(x))^2...

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