New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Indefinite Integrals question

2025 · 7 Apr · Shift 2 · Q48

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

PYQ Library
JEE Main
Mathematics
Indefinite Integrals
2025 · 7 Apr · Shift 2 · Q48

Indefinite Integrals question

2025 · 7 Apr · Shift 2 · Q48

JEE MainMathematicsIndefinite IntegralsNumerical+4 / −1

If

\int\left(\frac{1}{x}+\frac{1}{x^3}\right)\left(\sqrt[23]{3 x^{-24}+x^{-26}}\right) \mathrm{d} x=-\frac{\alpha}{3(\alpha+1)}\left(3 x^\beta+x^\gamma\right)^{\frac{\alpha+1}{\alpha}}+C, x\gt 0,(\alpha, \beta, \gamma \in \mathbf{Z})

, where C is the constant of integration, then

\alpha+\beta+\gamma

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

More from Indefinite Integrals

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
Let $I (x) = \int \frac{6}{s i n ^{2} x ( 1 - c o t x ) ^{2}} d x$ . If $I (0) = 3$ , then $I (\frac{π}{12})$ is equal to2024 · MCQ