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Prove that int(0)^(pi//4)2tan^(3)xdx=1-l...

Prove that `int_(0)^(pi//4)2tan^(3)xdx=1-log2`.

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The correct Answer is:
`2int_(0)^(pi//4)sec^(2)x*tanxdx-2int_(0)^(pi//4)tanxdx`
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ARIHANT PUBLICATION-INTEGRATION -PART V (QUESTIONS FOR PRACTICE) (1 MARK)
  1. Evaluate the following int(0)^(3)(dx)/(9+x^(2)).

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  2. What is the value of int(-1)^(1)(dx)/(1+x^(2)) ?

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  3. If int(0)^(a)(1)/(4+x^(2))dx=(pi)/(8), then find the value of a.

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  4. Evaluate the following integrals int(e)^(e^(2))(dx)/(xlogx).

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  5. Evaluate the following integrals int(0)^(1)(dx)/(sqrt(1+x^(2)))

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  6. Evaluate the following integrals int(0)^(pi//2)cosxe^(sinx)dx

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  7. Evaluate the following integrals int(0)^(1)xe^(x^(2))dx.

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  8. Evaluate the following integrals int(0)^(pi//2)(sinx)/(1+cos^(2)x)dx...

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  9. Evaluate the following integrals int(4)^(9)(sqrt(x))/((30-x^(3//2))^...

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  10. Evaluate the following integrals int(0)^(1)(dx)/(e^(x)+e^(-x)).

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  11. Write the value of int(0)^(pi//2)(sinx)/(sinx+cosx)dx

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  12. If int(2)^(3)f(z)dx=9, then write the value of int(2)^(3)f(phi(z))d(ph...

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  13. Evaluate int(0)^(4)[sqrt(x)]dx.

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  14. Evaluate int0^7 [x/3]dx

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  15. If int(1)^(2)f(x)dx=lamda, then what is the value of int(1)^(2)int(3-x...

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  16. Evaluate int(0)^(a)(sqrt(x))/(sqrt(x)+sqrt(a-x))dx

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  17. Evaluate int(-pi//3)^(pi//3)sin^(3)xdx.

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  18. Write the value of int(-pi//4)^(pi//4)sin^(5)xcosxdx

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  19. Prove that int(-1)^(1)log((2-x)/(2+x))dx=0

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  20. Prove that int(0)^(pi//4)2tan^(3)xdx=1-log2.

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