Integration Bee 2026-27

Practice integrals set by the NMN Research team.

Practice paper · Qualifiers

Problem set selection from NUST Math Nexus Team Research.

Questions: 24
Marks: Saved in this browser

Question 1
$\int \frac{x}{x ^{4} + x ^{2} + 1} d x$
Graph the integrand for Q01
Question 2
$\int \frac{e ^{x} ( 1 + x )}{cos ^{2} ( x e ^{x} )} d x$
Graph the integrand for Q02
Question 3
$\int \frac{1}{1 + cos x} d x$
Graph the integrand for Q03
Question 4
$\int (coth x - coth^{3} x) d x$
Graph the integrand for Q04
Question 5
$\int_{0}^{x} y^{3} e^{- y} d y$
Graph the integrand for Q05The integrand in y, drawn against x.
Question 6
$\int_{- π}^{π} ⌈ sin x ⌉ d x$
Graph the integrand for Q06
Question 7
$\int (ln x)^{2} d x$
Graph the integrand for Q07
Question 8
$\int (tan x + tan^{5} x) d x$
Graph the integrand for Q08
Question 9
$\int \frac{1}{4 x ^{2} - 9} d x$
Graph the integrand for Q09
Question 10
$\int_{0}^{l n 2} \frac{e ^{5 x} - e ^{x}}{e ^{4 x} + e ^{2 x}} d x$
Graph the integrand for Q10
Question 11
$\int sec^{3} x d x$
Graph the integrand for Q11
Question 12
$\int_{0}^{π /2} \frac{1}{1 + sin x} d x$
Graph the integrand for Q12
Question 13
$\int_{0}^{l n 5} (e^{x} + e^{- x})^{2} d x$
Graph the integrand for Q13
Question 14
$\int \frac{x ^{2}}{1 - x ^{2}} d x$
Graph the integrand for Q14
Question 15
$\int_{0}^{π /2} x (sin x - x cos x) d x$
Graph the integrand for Q15
Question 16
$\int_{0}^{1} x^{3} 1 - x^{2} d x$
Graph the integrand for Q16
Question 17
$\int_{0}^{π /2} \frac{sin x}{sin x + cos x} d x$
Graph the integrand for Q17
Question 18
$\int_{0}^{l n 2} \frac{1}{cosh x} d x$
Graph the integrand for Q18
Question 19
$\int_{0}^{l n 2} \frac{1}{1 + sinh x} d x$
Graph the integrand for Q19
Question 20
$\int_{l n 2}^{l n 4} x (1 - e^{- x}) d x$
Graph the integrand for Q20
Question 21
$\int x^{x} (1 + ln x) d x$
Graph the integrand for Q21
Question 22
$\int_{0}^{\infty} \frac{e ^{- 2 x} sin ( 3 x )}{x} d x$
Graph the integrand for Q22
Question 23
$\int_{0}^{\infty} \frac{e ^{- a x} - e ^{- b x}}{x} d x$
Graph the integrand for Q23Graphed with a = 1, b = 2.
Question 24
$\int_{2}^{4} \frac{ln ( 9 - x )}{ln ( 9 - x ) + ln ( 3 + x )} d x$
Graph the integrand for Q24

All Bee editions →

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23

Question 24