1
(i) \[\int \ln(x) \, dx\]
(ii) \[\int x \ln(x) \, dx\]
2
\[\int x^7 \ln(x) \, dx\]
3
(i) \[\int y^7 \ln y \, dy\]
(ii) \[\int x^5 \ln(2x) \, dx\]
(iii) \[\int x^2 \sin(x) \, dx\]
4
(i) \[\int x e^{2x} \, dx\]
(ii) \[\int x^2 e^{2x} \, dx\]
(iii) \[\int x^3 e^{2x} \, dx\]
5
(i) \[\int x \cos(x) \, dx\]
(ii) \[\int 5t e^{-5t} \, dt\]
6
\[\int \ln(\sqrt{x}) \, dx\]
7
(i) \[\int (x^2+1) \cos(2x) \, dx\]
(ii) \[\int (3x-5) e^x \, dx\]
8
(i) \[\int x e^{5x} \, dx\]
(ii) \[\int x^2 e^{-x} \, dx\]
9
(i) \[\int 5x \cos(3x) \, dx\]
(ii) \[\int (5x+2)\sin\left(\frac{x}{4}\right) \, dx\]
10
(i) \[\int x^2 \cos(2x) \, dx\]
(ii) \[\int x^3 \cos(2x) \, dx\]
11
\[\int x^2 \sin(x) \, dx\]
12
\[\int e^x \cos(x) \, dx\]
13
\[\int 6 \sin(3y) e^{2y} \, dy\]
14
\[\int \arcsin(x) \, dx\]
15
\[\int x^3 e^{x^2} \, dx\]
16
\[\int \tan^{-1}(2x) \, dx\]
17
\[\int_1^{\sqrt{3}} 8\arctan(1/x) \, dx\]
18
\[\int (\ln(x))^2 \, dx\]
19
(i) \[\int_0^1 (x^2+1) e^x \, dx\]
(ii) \[\int_0^{\pi/4} 2x \sin(2x) \, dx\]
20
\[\int \sin(\sqrt{x}) \, dx\]