New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Indefinite Integrals question

2025 · 4 Apr · Shift 2 · Q46

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

PYQ Library
JEE Main
Mathematics
Indefinite Integrals
2025 · 4 Apr · Shift 2 · Q46

Indefinite Integrals question

2025 · 4 Apr · Shift 2 · Q46

JEE MainMathematicsIndefinite IntegralsNumerical+4 / −1

If

\int \frac{\left(\sqrt{1+x^2}+x\right)^{10}}{\left(\sqrt{1+x^2}-x\right)^9} \mathrm{~d} x=\frac{1}{\mathrm{~m}}\left(\left(\sqrt{1+x^2}+x\right)^{\mathrm{n}}\left(\mathrm{n} \sqrt{1+x^2}-x\right)\right)+\mathrm{C}

where C is the constant of integration and

\mathrm{m}, \mathrm{n} \in \mathbf{N}

, then

\mathrm{m}+\mathrm{n}

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

More from Indefinite Integrals

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
If $\int \frac{2 x ^{2} + 5 x + 9}{x ^{2} + x + 1} d x = x x^{2} + x + 1 + α x^{2} + x + 1 + β lo g_{e} x + \frac{1}{2} + x^{2} + x + 1 + C$ , where $C$ is the constant of integration, then $α + 2 β$ …2025 · Numerical
If $f (x) = \int \frac{1}{x ^{1/4} ( 1 + x ^{1/4} )} d x, f (0) = - 6$ , then $f (1)$ is equal to :2025 · MCQ
If $\int cosec^{5} x d x = α cot x cosec x (cosec^{2} x + \frac{3}{2}) + β lo g_{x} tan \frac{x}{2} + C$ where $α, β \in R$ and $C$ is…2024 · Numerical
If $\int \frac{1}{a ^{2} s i n ^{2} x + b ^{2} c o s ^{2} x} d x = \frac{1}{12} tan^{- 1} (3 tan x) +$ constant, then the maximum value of $a sin x + b cos x$ , is :2024 · MCQ