New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Indefinite Integrals question

2024 · 4 Apr · Shift 2 · Q52

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

PYQ Library
JEE Main
Mathematics
Indefinite Integrals
2024 · 4 Apr · Shift 2 · Q52

Indefinite Integrals question

2024 · 4 Apr · Shift 2 · Q52

JEE MainMathematicsIndefinite IntegralsNumerical+4 / −1

If

\int \operatorname{cosec}^5 x d x=\alpha \cot x \operatorname{cosec} x\left(\operatorname{cosec}^2 x+\frac{3}{2}\right)+\beta \log _x\left|\tan \frac{x}{2}\right|+\mathrm{C}

where

\alpha, \beta \in \mathbb{R}

and

\mathrm{C}

is the constant of integration, then the value of

8(\alpha+\beta)

equals

\underline{\hspace{2cm}}

.

Numerical answer

More from Indefinite Integrals

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
If $\int \frac{1}{5 ( x - 1 ) ^{4} ( x + 3 ) ^{6}} d x = A (\frac{α x - 1}{β x + 3})^{B} + C$ , where $C$ is the constant of integration, then the value of $α + β + 20 AB$ is …2024 · Numerical
Let $\int \frac{2 - t a n x}{3 + t a n x} d x = \frac{1}{2} (α x + lo g_{e} ∣ β sin x + γ cos x ∣) + C$ , where $C$ is the constant of integration. Then $α + \frac{γ}{β}$ is equal to :2024 · MCQ
$The integral \int \frac{( x ^{8} - x ^{2} ) d x}{( x ^{12} + 3 x ^{6} + 1 ) t a n ^{- 1} ( x ^{3} + \frac{1}{x ^{3}} )} is equal to :$ 2024 · MCQ
For $x \in (- \frac{π}{2}, \frac{π}{2})$ , if $y (x) = \int \frac{cosec x + s i n x}{cosec x s e c x + t a n x s i n ^{2} x} d x$ , and $lim_{x \to (\frac{π}{2})^{-}} y (x) = 0$ then $y (\frac{π}{4})$ …2024 · MCQ
If $\int \frac{s i n ^{\frac{3}{2}} x + c o s ^{\frac{3}{2}} x}{s i n ^{3} x c o s ^{3} x s i n ( x - θ )} d x = A cos θ tan x - sin θ + B cos θ - sin θ cot x + C$ , where $C$ is the integration constant, then $A B$ …2024 · MCQ
Let $I (x) = \int \frac{x ^{2} ( x s e c ^{2} x + t a n x )}{( x t a n x + 1 ) ^{2}} d x$ . If $I (0) = 0$ , then $I (\frac{π}{4})$ is equal to :2023 · MCQ