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The primitive of the function f(x)=(1...

The primitive of the function `f(x)=(1-1/(x^2))a^(x+1/x)\ ,\ a >0` is `(a^(x+1/x))/((log)_e a)` (b) `(log)_e adota^(x+1/x)` (c) `(a^(x+1/x))/x(log)_e a` (d) `x(a^(x+1/x))/((log)_e a)`

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Let `t=x+1/x​⇒dt=(1−1/x^2​)dx`
`f′(x)=(1−1/x^2​)a^(x+1/x)`
​ ⇒`f′(x)=a^tdt`
⇒`f(x)=∫a^tdt`
...
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RD SHARMA-INDEFINITE INTEGRALS-Solved Examples And Exercises
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  2. int(sin^2x)/(cos^4x)\ dx= 1/3tan^2x+C (b) 1/2tan^2x+C (c) 1/3tan^3x+C...

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  5. intsqrt(x/(1-x))\ dx is equal to sin^(-1)sqrt(x)+C (b) sin^(-1){sqrt(x...

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  6. Evaluate: inte^x(f(x)+f^(prime)(x))dx=e^xf(x)+C

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  7. The value of int(sinx+cosx)/(sqrt(1-sin2x))\ dx is equal to sqrt(sin2x...

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  8. If intxsinx\ dx=-xcosx+alpha, then alpha is equal to sinx+C (b) cosx+C...

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  9. int(cos2x-1)/(cos2x+1)\ dx= tanx-x+C (b) x+tanx+C (c) x-tanx+C (d) ...

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  10. int(cos2x-cos2theta)/(cosx-costheta)\ dx is equal to 2\ (sinx+xcosthet...

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  11. int(x^9dx)/((4x^2+1)^9)i se q u a lto (a)1/(5x)(4+1/(x^2))^(-5)+c ...

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  12. int(x^3)/(sqrt(1+x^2))\ dx=a(1+x^2)^(3setminus2)+bsqrt(1+x^2)+C , then...

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  13. int(x^3)/(x+1)\ dx is equal to x+(x^2)/2+(x^3)/3-log|1-x|+C (b) x+(x^...

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  14. Ifint(dx)/((x+2)(x^2+1))=aln(1+x^2)+btan^(-1)x+1/5ln|x+2|+C Then a=1/...

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  15. Evaluate: int1/(sqrt(x)+sqrt(x+1))\ dx

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  16. Evaluate: int(1-x^4)/(1-x)\ dx

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  17. Evaluate: int(x+2)/((x+1)^3)\ dx

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  18. Evaluate int ((8x+13)/sqrt(4x+7)) dx (A) 1/3 (4x+7)^(3/2) - 1/2 (4x+7)...

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  19. Evaluate: int(1+x+x^2)/(x^2(1+x))\ dx

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  20. Evaluate: int((2^x+3^x)^2)/(6^x)\ dx

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