New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Indefinite Integrals question

2005 · Shift 0 · Q78

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Indefinite Integrals
2005 · Shift 0 · Q78

Indefinite Integrals question

2005 · Shift 0 · Q78

JEE MainMathematicsIndefinite IntegralsMCQ+4 / −1

\int {{{\left\{ {{{\left( {\log x - 1} \right)} \over {1 + {{\left( {\log x} \right)}^2}}}} \right\}}^2}\,\,dx}

is equal to

A
${{\log x} \over {{{\left( {\log x} \right)}^2} + 1}} + C$
B
${x \over {{x^2} + 1}} + C$
C
${{x{e^x}} \over {1 + {x^2}}} + C$
D
${x \over {{{\left( {\log x} \right)}^2} + 1}} + C$

More from Indefinite Integrals

If $\int \frac{s i n x}{s i n ( x - α )} d x = A x + B lo g sin (x - α), + C,$ then value of $(A, B)$ is2004 · MCQ
$\int \frac{d x}{c o s x - s i n x}$ is equal to2004 · MCQ
$Let f (x) = \int x^{3} 3 - x^{2} d x . If 5 f (2) = - 4, then f (1) is equal to$ 2025 · MCQ
If $\int \frac{( 1 + x ^{2} + x ) ^{10}}{( 1 + x ^{2} - x ) ^{9}} d x = \frac{1}{m} ((1 + x^{2} + x)^{n} (n 1 + x^{2} - x)) + C$ where C is the…2025 · Numerical
If $\int (\frac{1}{x} + \frac{1}{x ^{3}}) (23 3 x^{- 24} + x^{- 26}) d x = - \frac{α}{3 ( α + 1 )} (3 x^{β} + x^{γ})^{\frac{α + 1}{α}} + C, x > 0, (α, β, γ \in Z)$ ,…2025 · Numerical
If $\int e^{x} (\frac{x s i n ^{- 1} x}{1 - x ^{2}} + \frac{s i n ^{- 1} x}{( 1 - x ^{2} ) ^{3/2}} + \frac{x}{1 - x ^{2}}) d x = g (x) + C$ , where C is the constant of integration, then $g (\frac{1}{2})$ …2025 · MCQ
Let $I (x) = \int \frac{d x}{( x - 11 ) ^{\frac{11}{13}} ( x + 15 ) ^{\frac{15}{13}}}$ . If $I (37) - I (24) = \frac{1}{4} (\frac{1}{b ^{\frac{1}{13}}} - \frac{1}{c ^{\frac{1}{13}}}), b, c \in N$ …2025 · MCQ
Let $\int x^{3} sin x d x = g (x) + C$ , where $C$ is the constant of integration. If $8 (g (\frac{π}{2}) + g^{'} (\frac{π}{2})) = α π^{3} + β π^{2} + γ, α, β, γ \in Z$ , then $α + β - γ$ …2025 · MCQ