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Evaluate: If intcos^nxdotdx prove that I...

Evaluate: If `intcos^nxdotdx` prove that `I_n=1/n(cos^(n-1)xsinx)+((n-1)/n)I_(n-2)`

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CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. Evaluateintsqrt(secx-1)dx, 0ltxltpi/2

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  2. Evaluate: int((1-xsinx)dx)/(x(1-x^3e^(3cosx)))

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  3. Evaluate: If intcos^nxdotdx prove that In=1/n(cos^(n-1)xsinx)+((n-1)/n...

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  4. Evaluate : int (xdx)/sqrt(1+x^4)

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  5. Evaluate: int(e^(tan^(-1)x))/((1+x^2))[(sec^(-1)sqrt(1+x^2)+cos^(-1)(...

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  6. int(sqrt(x-1))/(xsqrt(x+1))dx is e q u a l to ln|x-sqrt(x^...

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  7. IfI=int(dx)/((2a x+x^2)^(3/2)),then I is equal to (a)-(x+a)/(sqrt(2a ...

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  8. If f^(prime)(x)=1/(-x+sqrt(x^2+1)) and f(0)=(1+sqrt(2))/2 then f(1) ...

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  9. inte^x((2tanx)/(1+tanx)+cot^2(x+pi/4))dx is equal to (a)e^xtan(pi/4-x...

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  10. The value of the integral int(x^2+x)(x^(-8)+2x^(-9))^(1/(10))dx is 5/(...

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

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  12. If int (3sinx+2cosx)/ (3cosx+2sinx) dx=a x+b ln|2sinx+3cosx|+C, then (...

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  13. Ifint(3e^x-5e^(-x))/(4e^x+5e^(-x))dx=a x+bln(4e^x+5e^(-x))+C ,t h e n ...

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  14. If intsqrt((cosx-cos^3x)/((1-cos^3x)))dx=f(x)+c, then f(x) is equal to

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  15. If l^r(x) means logloglog...... x , the log being repeated r times, th...

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  16. I=int(cos4x+1)/(cotx-tanx)dx is equal to ?

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  17. If int(dx)/(sqrt(sin^3xcos^5x))=asqrt(cotx)+bsqrt(tan^3)x+c , then (...

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  18. int e^(tan^(-1)x)(1+x+x^2)d(cot^(-1)x) is equal to (a) -e^(tan^(-1)x)...

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  19. int(x^9dx)/((4x^2+1)^6) is equal to (a)1/(5x)(4+1/(x^2))^(-5)+c (b...

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  20. int(2sinx)/(3+sin2x)dx is equal to

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