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Integrate the functions cos^(3)xe^(log...

Integrate the functions
`cos^(3)xe^(logsinx)`

Text Solution

Verified by Experts

The correct Answer is:
`-1/4cos^(4)x+C`
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NCERT GUJARATI-INTEGRALS-EXERCISE 7.12
  1. Integrate the functions (e^(x))/((1+e^(x))(2+e^(x)))

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  2. Integrate the functions 1/((x^(2)+1)(x^(2)+4))

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  3. Integrate the functions cos^(3)xe^(logsinx)

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  4. Integrate the functions e^(3logx)(x^(4)+1)^(-1)

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  5. Integrate the functions f'(ax+b)[f(ax+b)]^(n)

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  6. Integrate the functions 1/(sqrt(sin^(3)xsin(x+alpha))

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  7. Integrate the functions (sin^(-1)sqrtx-cos^(-1)sqrtx)/(sin^(-1)sqrtx...

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  8. Integrate the functions sqrt((1-sqrtx)/(1+sqrtx))

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  9. Integrate the functions (2+sin2x)/(1+cos2x)e^(x)

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  10. Integrate the functions (x^(2)+x+1)/((x+1)^(2)(x+2))

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  11. Integrate the functions tan^(-1)sqrt((1-x)/(1+x))

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  12. Integrate the functions (sqrt(x^(2)+1)[log(x^(2)+1)-2logx])/(x^(4))

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  13. Evaluate the definite integrals int(pi/2)^(pi)e^(x)((1-sinx)/(1-cosx...

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  14. Evaluate the definite integrals int(0)^(pi/4)(sinxcosx)/(cos^(4)x+si...

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  15. Evaluate the definite integrals int(0)^(pi/2)(cos^(2)xdx)/(cos^(2)x+...

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  16. Evaluate the definite integrals int(pi/6)^(pi/3)(sinx+cosx)/(sqrt(si...

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  17. Evaluate the definite integrals int(0)^(1)(dx)/(sqrt(1+x)-sqrtx)

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  18. Evaluate the definite integrals int(0)^(pi/4)(sinx+cosx)/(9+16sin2x)...

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  19. Evaluate the definite integrals int(0)^(pi/2)sin2xtan^(-1)(sinx)dx

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  20. Evaluate the definite integrals int(0)^(pi)(xtanx)/(secx+tanx)dx

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