JEE MAIN Indefinite Integration Previous Year Questions (PYQs) – Page 4 of 5
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The integral $\int {{1 \over {\root 4 \of {{{(x - 1)}^3}{{(x + 2)}^5}} }}} \,dx$ is equal to : (where C is a constant of integration)
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Solution
The integral
$ \displaystyle \int \frac{2x^{12} + 5x^{9}}{(x^{5} + x^{2} + 1)^{3}}, dx $
is equal to:
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Solution
If $\int {{{\sin }^{ - 1}}\left( {\sqrt {{x \over {1 + x}}} } \right)} dx$ = A(x)${\tan ^{ - 1}}\left( {\sqrt x } \right)$ + B(x) + C,
where C is a constant of integration, then theordered pair (A(x), B(x)) can be :
where C is a constant of integration, then theordered pair (A(x), B(x)) can be :
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Solution
The integral $\int {{{\left( {{x \over {x\sin x + \cos x}}} \right)}^2}dx} $ is equal to
(where C is a constant of integration):
(where C is a constant of integration):
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Solution
Let $f(x) = \int x^3 \sqrt{3 - x^2} , dx.$ If $5f(\sqrt{2}) = -4$, then $f(1)$ is equal to
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Solution
The integral $\int\limits_{{\pi \over 6}}^{{\pi \over 3}} {{{\tan }^3}x.{{\sin }^2}3x\left( {2{{\sec }^2}x.{{\sin }^2}3x + 3\tan x.\sin 6x} \right)dx} $is equal to:
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Solution
If
$\displaystyle \int \frac{dx}{\cos^{3}x\sqrt{2\sin 2x}} = (\tan x)^{A} + C(\tan x)^{B} + k,$
where $k$ is a constant of integration, then $A + B + C$ equals :
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Solution
If $\displaystyle \int \frac{dx}{(x^{2}-2x+10)^{2}} = A\left(\tan^{-1}\left(\frac{x-1}{3}\right) + \frac{f(x)}{x^{2}-2x+10}\right) + C$ where $C$ is a constant of integration, then:
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Solution
If $f(x)=\displaystyle\int \frac{5x^{8}+7x^{6}}{(x^{2}+1+2x^{7})^{2}}\,dx,\ (x\ge 0)$ and $f(0)=0$, then the value of $f(1)$ is:
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Solution
If$\int {\left( {{e^{2x}} + 2{e^x} - {e^{ - x}} - 1} \right){e^{\left( {{e^x} + {e^{ - x}}} \right)}}dx} $ = $g\left( x \right){e^{\left( {{e^x} + {e^{ - x}}} \right)}} + c$where c is a constant of integration,then g(0) is equal to :
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Solution
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