Find the values of the following integra...

Find the values of the following integrals
(iv) `int_(0)^(pi/4) sec^(3) x dx`

A

`1/2 ln 2`

B

`(1)/(sqrt(2))+1/2 ln (sqrt(2)+1)`

C

`(1)/(sqrt(2))- ln (sqrt(2)+1)`

D

`ln (sqrt(2)+1)`

Verified by Experts

The correct Answer is:

B

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int(0)^(pi//4) tan^(6) x dx=
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If I(n) = int(0)^(pi//4) tan^(n) x dx then (1)/(I(3)+I(5))=
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Find the values of the following integrals (iv) int(0)^(pi/4) sec^(...
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Find the values of the following integrals (ii) int(0)^(pi) cos^(3)...
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int(0)^(2pi) cos^(7) x sin^(5) x dx=
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{:(" " Lt),(x rarr0):}(int(0)^(x) sin^(3) t dt)/(x^(4))=
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Lt(xtoo)((int(0)^(x)cos^(3)tdt)/(x))=
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int(0)^(1) (x^(6))/(sqrt(1-x^(2)))dx=
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int(0)^(a)(a^(2)-x^(2))^(5//2)dx=
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int(0)^(2a) sqrt(2ax - x^(2)) dx=
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int(0)^(oo) (dx)/((1+x^(2))^(4))=
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int(0)^(pi//4) (Tan^(n)(x-[x])+Tan^(n-2)(x-[x]))dx
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int(0)^(2pi) x cos^(6) x dx=
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int(0)^(2pi) x sin^(4) x cos^(6) x dx=
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If I(n)= int(1)^(e) (log x)^(n) dx then I(8) + 8I(7)=
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If f(x)=Ax^(2) +Bx satisfies the conditions f^(1)(1)=8 and int(0)^(1) ...
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If I(1) = int(x)^(1) (1)/(1+t^(2))dt and I(2)=int(1)^(1/x) (1)/(1+t^(2...
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If I(1)=int(e)^(e^(2))(dx)/(logx)andI(2)=int(1)^(2)(e^(x))/(x)dx, then
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If I=int(0)^(1)sqrt(1+x^(3))dx then
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{:(" " Lt),( x rarr 0):} int(0)^(x^(2))(sin sqrt(t)dt)/(x^(3))=
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