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inte^x(1-cotx+cot^2x)dx= e^xcotx+C (b) ...

`inte^x(1-cotx+cot^2x)dx=` `e^xcotx+C` (b) ` e^xcotx+C` (c) `e^x\ cos e c\ x+C` (d) ` e^x\ cos e c\ x+C`

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`I=∫e^x(1−cotx+cot^2x)dx `
`I=∫e^x(1+cot^2x)dx−∫e^xcotxdx`
`I=∫e^xcosec^2xdx−∫e^xcotxdx`
Integrating by parts, we get
...
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RD SHARMA-INDEFINITE INTEGRALS-Solved Examples And Exercises
  1. 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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  2. Evaluate: int(cossqrt(x))/(sqrt(x))\ dx

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  3. inte^x(1-cotx+cot^2x)dx= e^xcotx+C (b) e^xcotx+C (c) e^x\ cos e c\ ...

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  4. int(sin^6x)/(cos^8x)\ dx= tan7x+C (b) (tan^7x)/7+C (c) (tan7x)/7+C (d...

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  5. int1/(7+5cosx)\ dx= 1/(sqrt(6))tan^(-1)(1/(sqrt(6))tanx/2)+C (b) 1/(s...

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  6. int1/(1+cosx+sinx)\ dx= log|1+cotx/2|+C (b) log|1-tanx/2|+C (c) log|...

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  7. int(x+3)/((x+4)^2)e^x\ dx= (e^x)/(x+4)+C (b) (e^x)/(x+3)+C (c) 1/((x+...

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  8. int(sinx)/(3+4cos^2x)\ dx log(3+4cos^2x)+C (b) 1/(2sqrt(3))tan^(-1)((...

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  9. int e^x ((1-sinx)/(1-cosx)) dx= (A) e^xtan(x/2)+C (B) e^xcot(x/...

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  10. int2/((e^x+e^(-x))^2)\ dx ( e^(-x))/(e^x+e^(-x))+C (b) -1/(e^x+e^(-x)...

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  11. int(e^x(1+x))/(cos^2(x e^x))\ dx= 2(log)ecos(x e^x)+C (b) sec(x e^x)+...

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  12. int(sin^2x)/(cos^4x)\ dx= 1/3tan^2x+C (b) 1/2tan^2x+C (c) 1/3tan^3x+C...

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  13. The primitive of the function f(x)=(1-1/(x^2))a^(x+1/x)\ ,\ a >0 is...

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  14. The value of int1/(x+xlogx)\ dx is 1+logx (b) x+logx (c) xlog(1+logx)...

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

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

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

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

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

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

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