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If I=intsec^2xcos e c^4x dx=Acot^3x+Btan...

If `I=intsec^2xcos e c^4x dx=Acot^3x+Btanx+Ccotx+D ,` then find the values of A,B,C and D.

A

`A=-(1)/(3)`

B

`B=2`

C

`C=-2`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A, C
`I=int sec^(2)x "cosec"^(4)xdx`
`=int((sin^(2)x+cos^(2)x)^(2))/(cos^(2)xsin^(4)x)dx`
`=int(sin^(4)x+cos^(4)x+2sin^(2)x cos^(2)x)/(cos^(2)xsin^(4)x)dx`
`=int(sec^(2)x+2"cosec"^(2)x+(cos^(2)x)/(sin^(4)x))dx `
`=tanx-2cotx+int cot^(2)x"cosec"^(2)x dx`
`=tanx-2cotx-(cot^(3)x)/(3)+D`
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CENGAGE PUBLICATION-INDEFINITE INTEGRATION-Exercises (Multiple Correct Answers Type)
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  2. If intsinx d(secx)=f(x)-g(x)+c ,t h e n f(x)=secx (b) f(x)=tanx g(x...

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  3. Evaluate: int sqrt(1+cosecx dx)

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  4. If I=intsec^2xcos e c^4x dx=Acot^3x+Btanx+Ccotx+D , then find the valu...

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  5. A curve g(x)=intx^(27)(1+x+x^2)^6(6x^2+5x+4)dx is passing through orig...

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  6. If int (sqrtx)^5/((sqrtx)^7+x^6) dx= alog(x^k/(1+x^k))+c then a and k ...

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  7. If I=int(sinx+sin^3x)/(cos2x)dx=Pcosx+Qlog|f(x)|+R , then P=1/2,Q=-3/(...

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  8. If int(e^(x-1))/((x^2-5x+4))2xdx=A F(x-1)+B F(x-4)+C and F(x)=int(e^x)...

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  9. If intx^2dote^(-2x)dx=e^(-2x)(a x^2+b x+c)+d , then the value of |a/(b...

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  10. Ifint(x^4+1)/(x^6+1)dx=tan^(-1)f(x)-2/3tan^(-1)g(x)+C ,t h e n a) bo...

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  11. If int(x^2-x+1)/((x^2+1)^(3/2))e^x dx=e^xf(x)+c, then (a) f(x) is an ...

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  12. If int(cos4x+1)/(cotx-tanx)dx = Acos4x+B ,t h e n (a)A=-1/8 (b) B=1/...

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  13. If intsin^(-1)xcos^(-1)xdx=f^(-1)(x)[π/2x-xf^(-1)(x)-2sqrt(1-x^2)]+2x+...

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  14. If f(x)=int(x^8+4)/(x^4-2x^2+2)dxa n df(0)=0,t h e n f(x) is an odd f...

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  15. If int(dx)/(x^2+a x+1)=f(g(x))+c , then f(x) is inverse trigonometric ...

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  16. If int((1-x^7))/(x(1+x^7))dx=Plogabsx+Qlogabs(x^7+1)+c

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

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