Indefinite Integrals — JEE Main PYQs

92 previous year questions on Indefinite Integrals (Mathematics), newest first. Open any question for its complete step-by-step solution.

For real numbers $α, β, γ$ and $δ$ , if $\int \frac{( x ^{2} - 1 ) + t a n ^{- 1} ( \frac{x ^{2} + 1}{x} )}{( x ^{4} + 3 x ^{2} + 1 ) t a n ^{- 1} ( \frac{x ^{2} + 1}{x} )} d x$ …
JEE Main 2021View solution →
Let $I_{n} = \int_{1}^{e} x^{19} (lo g ∣ x ∣)^{n} d x$ , where $n \in N$ . If (20) $l_{10} = α l_{9} + β l_{8}$ , for natural numbers $α$ and $β$ then $α - β$ equals to ______.
JEE Main 2021View solution →
The integral $\int \frac{( 2 x - 1 ) c o s ( 2 x - 1 ) ^{2} + 5}{4 x ^{2} - 4 x + 6} d x$ is equal to : (where c is a constant of integration)
JEE Main 2021View solution →
If $f (x) = \int \frac{5 x ^{8} + 7 x ^{6}}{( x ^{2} + 1 + 2 x ^{7} ) ^{2}} d x, (x \geq 0), f (0) = 0$ and $f (1) = \frac{1}{K}$ , then the value of $K$ is
JEE Main 2021View solution →
If $\int \frac{c o s x d x}{s i n ^{3} x ( 1 + s i n ^{6} x ) ^{2/3}} = f (x) (1 + sin^{6} x)^{1/ λ} + c$ where $c$ is a constant of integration, then $λ f (\frac{π}{3})$ is equal to:
JEE Main 2020View solution →
If $\int \frac{d θ}{c o s ^{2} θ ( t a n 2 θ + s e c 2 θ )} = λ tan θ + 2 lo g_{e} ∣ f (θ) ∣ + C$ where $C$ is a constant of integration, then the ordered pair $(λ, f (θ))$ is equal to:
JEE Main 2020View solution →
If $f^{'} (x) = tan^{- 1} (sec x + tan x), - \frac{π}{2} < x < \frac{π}{2}$ , and $f (0) = 0$ , then $f (1)$ is equal to:
JEE Main 2020View solution →
The integral $\int \frac{dx}{( x + 4 ) ^{8/7} ( x - 3 ) ^{6/7}}$ is equal to:
(where $C$ is a constant of integration)
JEE Main 2020View solution →
If $\int \frac{c o s θ}{5 + 7 s i n θ - 2 c o s ^{2} θ} d θ = A lo g_{e} ∣ B (θ) ∣ + C$ , where $C$ is a constant of integration, then $\frac{B ( θ )}{A}$ can be:
JEE Main 2020View solution →
If the value of the integral $\int_{0}^{1/2} \frac{x ^{2}}{( 1 - x ^{2} ) ^{3/2}} d x$ is $\frac{k}{6}$ , then $k$ is equal to:
JEE Main 2020View solution →
If $\int sin^{- 1} (\frac{x}{1 + x}) d x = A (x) tan^{- 1} (x) + B (x) + C$ , where $C$ is a constant of integration, then the ordered pair $(A (x), B (x))$ can be:
JEE Main 2020View solution →
The integral $\int_{1}^{2} e^{x} \cdot x^{2} (2 + lo g_{e} x) d x$ equals:
JEE Main 2020View solution →
If …
JEE Main 2020View solution →
The integral $\int (\frac{x}{x s i n x + c o s x})^{2} d x$ is equal to (where $C$ is constant of integration):
JEE Main 2020View solution →
Let $f (x) = \int \frac{x}{( 1 + x ) ^{2}} d x (x \geq 0)$ . Then $f (3) - f (1)$ is equal to:
JEE Main 2020View solution →
$\int \frac{s i n \frac{5 x}{2}}{s i n \frac{x}{2}} d x$ is equal to:
(where c is a constant of integration).
JEE Main 2019View solution →
If $\int \frac{d x}{x ^{3} ( 1 + x ^{6} ) ^{2/3}} = x f (x) (1 + x^{6})^{\frac{1}{3}} + C$ where $C$ is a constant of integration, then the function $f (x)$ is equal to:
JEE Main 2019View solution →
The integral $\int sec^{2/3} x cosec^{4/3} x d x$ is equal to: (Here $C$ is a constant of integration)
JEE Main 2019View solution →
Let $n \geq 2$ be a natural number and $0 < θ < π /2$ . Then $\int \frac{( s i n ^{n} θ - s i n θ ) ^{\frac{1}{n}} c o s θ}{s i n ^{n + 1} θ} d θ$ is equal to: (where C is a constant of integration)
JEE Main 2019View solution →
If $\int \frac{x + 1}{2 x - 1} d x = f (x) 2 x - 1 + C$ , where $C$ is a constant of integration, then $f (x)$ is equal to:
JEE Main 2019View solution →
The integral $\int \frac{2 x ^{3} - 1}{x ^{4} + x} d x$ is equal to:
(Here C is a constant of integration)
JEE Main 2019View solution →
If $\int x^{5} e^{- x^{2}} d x = g (x) e^{- x^{2}} + c$ , where $c$ is a constant of integration, then $g (- 1)$ is equal to
JEE Main 2019View solution →
If $\int \frac{1 - x ^{2}}{x ^{4}} d x = A (x) (1 - x^{2})^{m} + C$ , for a suitable chosen integer $m$ and a function $A (x)$ , where $C$ is a constant of integration, then $(A (x))^{m}$ equals:
JEE Main 2019View solution →
The integral $\int cos (lo g_{e} x) d x$ is equal to: (where $C$ is a constant of integration)
JEE Main 2019View solution →
Let $α \in (0, π /2)$ be fixed. If the integral $\int \frac{t a n x + t a n α}{t a n x - t a n α} d x = A (x) cos 2 α + B (x) sin 2 α + C$ , where $C$ is a constant of integration, then the functions $A (x)$ and $B (x)$ are respectively:
JEE Main 2019View solution →
The integral $\int \frac{3 x ^{13} + 2 x ^{11}}{( 2 x ^{4} + 3 x ^{2} + 1 ) ^{4}} d x$ is equal to (where $C$ is a constant of integration)
JEE Main 2019View solution →
If $\int e^{s e c x} (sec x + tan x f (x) + (sec x tan x + sec^{2} x)) d x = e^{s e c x} f (x) + C$ , then a possible choice of $f (x)$ is
JEE Main 2019View solution →
If $f (x) = \int \frac{5 x ^{8} + 7 x ^{6}}{( x ^{2} + 1 + 2 x ^{7} ) ^{2}} d x, (x \geq 0)$ and $f (0) = 0$ , then the value of $f (1)$ is:
JEE Main 2019View solution →
For $x^{2} \neq = nπ + 1, n \in N$ (the set of natural numbers), the integral
$\int x \cdot \frac{2 s i n ( x ^{2} - 1 ) - s i n 2 ( x ^{2} - 1 )}{2 s i n ( x ^{2} - 1 ) + s i n 2 ( x ^{2} - 1 )} d x$ is
JEE Main 2019View solution →
If $\int \frac{d x}{( x ^{2} - 2 x + 10 ) ^{2}}$
$= A (tan^{- 1} (\frac{x - 1}{3}) + \frac{f ( x )}{x ^{2} - 2 x + 10}) + C$
Where $C$ is a constant of integration, then:
JEE Main 2019View solution →
The integral
$\int \frac{s i n ^{2} x c o s ^{2} x}{( s i n ^{5} x + c o s ^{3} x s i n ^{2} x + s i n ^{3} x c o s ^{2} x + c o s ^{5} x ) ^{2}} d x$ is equal to :
JEE Main 2018View solution →
Let $I_{n} = \int tan^{n} x d x, (n > 1) .$ If $I_{4} + I_{6} = a tan^{5} x + b x^{5} + C$ , where C is a constant of integration, then the ordered pair $(a, b)$ is equal to :
JEE Main 2017View solution →
The integral $\int \frac{2 x ^{12} + 5 x ^{9}}{( x ^{5} + x ^{3} + 1 ) ^{3}} dx$ is equal to:
JEE Main 2016View solution →
The integral $\int \frac{dx}{x ^{2} ( x ^{4} + 1 ) ^{3/4}}$ equals :
JEE Main 2015View solution →
The integral $\int (1 + x - \frac{1}{x}) e^{x + \frac{1}{x}} d x$ is equal to
JEE Main 2014View solution →
If $\int f (x) d x = Ψ (x)$ , then $\int x^{5} f (x^{3}) d x$ is equal to
JEE Main 2013View solution →
If the integral $\int \frac{5 t a n x}{t a n x - 2} d x = x + a ln ∣ sin x - 2 cos x ∣ + k$ , then a is equal to
JEE Main 2012View solution →
The value of $2 \int \frac{s i n x d x}{s i n ( x - \frac{π}{4} )}$ is
JEE Main 2008View solution →
$\int \frac{d x}{c o s x + 3 s i n x}$ equals
JEE Main 2007View solution →
$\int {\frac{( l o g x - 1 )}{( 1 + ( l o g x ) ^{2}}}^{2} d x$ is equal to
JEE Main 2005View solution →
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 $(A, B)$ is
JEE Main 2004View solution →
$\int \frac{d x}{c o s x - s i n x}$ is equal to
JEE Main 2004View solution →