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If inte^x\ (tanx+1)secx\ dx=e^x\ f(x)+C ...

If `inte^x\ (tanx+1)secx\ dx=e^x\ f(x)+C` , then write the value of `f(x)` .

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We know that,
`int e^x f(x)+ int e^x f'(x)=e^x f(x)+C`

Given that,

`inte^x\ (tanx+1)secx\ dx=e^x\ f(x)+C`

`inte^x sec x+int e^x tanx sec x=e^x secx +C`

`f(x)=secx`
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RD SHARMA-INDEFINITE INTEGRALS-Solved Examples And Exercises
  1. Evaluate: int(x+cos6x)/(3x^2+sin6x)\ dx

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  2. If int((x-1)/(x^2))e^x\ dx=f(x)\ e^x+C , then write the value of f(...

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  3. If inte^x\ (tanx+1)secx\ dx=e^x\ f(x)+C , then write the value of f...

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  4. Evaluate: int(2)/(1-cos2x)\ dx

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  5. Write the anti derivative of (3sqrt(x)+1/(sqrt(x))) .

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  6. Evaluate: intcos^(-1)(sinx)\ dx

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  7. Evaluate: int1/(sin^2xcos^2x)\ dx

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  8. intx/(4+x^4)\ dx is equal to 1/4tan^(-1)x^2 (b) 1/4tan^(-1)((x^2)/2) (...

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  9. int1/(cosx+sqrt(3)sinx)\ dx is equal to logtan(pi/3+x/2)+C (b) logtan(...

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  10. intxsecx^2\ dx is equal to 1/2log(secx^2+tanx^2)+C (b) (x^2)/2log(secx...

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  11. If int1/(5+4sinx)\ dx=Atan^(-1)(Btanx/2+4/3)+C , then A=2/3,\ \ B=5/3 ...

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  12. intx^(sinx) ((sinx)/x+cosxdotlogx) dx is equal to (A) x^(sinx)+C (B...

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  13. Integration of 1/(1+((log)e x)^2) with respect to (log)e x is (tan^(-1...

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  14. int(cos8x-1)/(tan2x-cot2x)dx

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  15. If int(sin^8x-cos^8x)/(1-2sin^2xcos^2x)dx=asin2x+C , then a= -1//2 (b...

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  16. int(x-1)\ e^(-x)\ dx is equal to x e^x+C (b) x e^x+C (c) -x e^(-x)+C ...

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  17. If int(2^(1setminusx))/(x^2)\ dx=k\ 2^(1setminusx)+C , then k is equal...

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  18. int1/(1+tanx)\ dx=

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  19. int|x|^3\ dx is equal to ( x^4)/4+C (b) (|x|^4)/4+C (c) (x^4)/4+C (d) ...

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  20. Evaluate: int(cossqrt(x))/(sqrt(x))\ dx

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