[
next
] [
prev
] [
prev-tail
] [
tail
] [
up
]
3.5
Integrals 401 to 500
3.5.1
\(\int \genfrac {}{}{}{}{\tan (x)}{(-1+\sqrt {\tan (x)})^2} \, dx\) [401]
3.5.2
\(\int \genfrac {}{}{}{}{\sin (x)}{\sqrt {\sin (2 x)}} \, dx\) [402]
3.5.3
\(\int \genfrac {}{}{}{}{\cos (x)}{\sqrt {\sin (2 x)}} \, dx\) [403]
3.5.4
\(\int \sin (x) \sqrt {\sin (2 x)} \, dx\) [404]
3.5.5
\(\int (\cos (x)-\sin (x)) \sqrt {\sin (2 x)} \, dx\) [405]
3.5.6
\(\int \genfrac {}{}{}{}{\sin ^7(x)}{\sin ^{\genfrac {}{}{}{}{7}{2}}(2 x)} \, dx\) [406]
3.5.7
\(\int \genfrac {}{}{}{}{\cos ^7(x)}{\sin ^{\genfrac {}{}{}{}{7}{2}}(2 x)} \, dx\) [407]
3.5.8
\(\int \csc ^5(x) \sin ^{\genfrac {}{}{}{}{3}{2}}(2 x) \, dx\) [408]
3.5.9
\(\int \genfrac {}{}{}{}{\sec ^3(x)}{\sqrt {\sin (2 x)}} \, dx\) [409]
3.5.10
\(\int \genfrac {}{}{}{}{\csc (x)}{\sin ^{\genfrac {}{}{}{}{3}{2}}(2 x)} \, dx\) [410]
3.5.11
\(\int \genfrac {}{}{}{}{\cos ^3(x) (\cos (2 x)-3 \tan (x))}{(\sin ^2(x)-\sin (2 x)) \sin ^{\genfrac {}{}{}{}{5}{2}}(2 x)} \, dx\) [411]
3.5.12
\(\int \sqrt {\sec ^4(x) \tan (x)} \, dx\) [412]
3.5.13
\(\int \sqrt {\sin ^4(x) \tan (x)} \, dx\) [413]
3.5.14
\(\int \sqrt [3]{\sec ^{12}(x) \tan ^2(x)} \, dx\) [414]
3.5.15
\(\int \genfrac {}{}{}{}{1}{\sqrt [4]{\cos ^{11}(x) \sin ^{13}(x)}} \, dx\) [415]
3.5.16
\(\int \genfrac {}{}{}{}{\cos (2 x)-\sqrt {\sin (2 x)}}{\sqrt {\cos ^3(x) \sin (x)}} \, dx\) [416]
3.5.17
\(\int \genfrac {}{}{}{}{\sqrt {\cos (x) \sin ^3(x)}-2 \sin (2 x)}{-\sqrt {\cos ^3(x) \sin (x)}+\sqrt {\tan (x)}} \, dx\) [417]
3.5.18
\(\int \genfrac {}{}{}{}{-3 \tan (x)+\sqrt [3]{\sec ^6(x) \tan (x)}}{(\cos ^5(x) \sin (x))^{2/3}} \, dx\) [418]
3.5.19
\(\int (1+2 \cos ^2(x))^{5/2} \sin (x) \, dx\) [419]
3.5.20
\(\int \cos (x) (5 \cos ^2(x)+\sin ^2(x))^{5/2} \, dx\) [420]
3.5.21
\(\int \cos (x) (-\cos ^2(x)-5 \sin ^2(x))^{3/2} \, dx\) [421]
3.5.22
\(\int \genfrac {}{}{}{}{\sin (x)}{(5 \cos ^2(x)-2 \sin ^2(x))^{7/2}} \, dx\) [422]
3.5.23
\(\int \genfrac {}{}{}{}{\cos (x) \cos (2 x)}{(2-5 \sin ^2(x))^{3/2}} \, dx\) [423]
3.5.24
\(\int \genfrac {}{}{}{}{\sin (5 x)}{(5 \cos ^2(x)+9 \sin ^2(x))^{5/2}} \, dx\) [424]
3.5.25
\(\int \genfrac {}{}{}{}{\cos (x) \cos (2 x) \sin (3 x)}{(-5+4 \sin ^2(x))^{5/2}} \, dx\) [425]
3.5.26
\(\int \genfrac {}{}{}{}{\csc ^2(x) (-2 \cos ^3(x) (-1+\sin (x))+\cos (2 x) \sin (x))}{\sqrt {-5+\sin ^2(x)}} \, dx\) [426]
3.5.27
\(\int \genfrac {}{}{}{}{\cos (3 x)}{-\sqrt {-1+8 \cos ^2(x)}+\sqrt {3 \cos ^2(x)-\sin ^2(x)}} \, dx\) [427]
3.5.28
\(\int (2-3 \sin ^2(x))^{3/5} \sin (4 x) \, dx\) [428]
3.5.29
\(\int \cos (x) \sqrt {\cos (2 x)} \, dx\) [429]
3.5.30
\(\int \cos ^{\genfrac {}{}{}{}{3}{2}}(2 x) \sin (x) \, dx\) [430]
3.5.31
\(\int \genfrac {}{}{}{}{\sin (x)}{\cos ^{\genfrac {}{}{}{}{5}{2}}(2 x)} \, dx\) [431]
3.5.32
\(\int \cos ^{\genfrac {}{}{}{}{3}{2}}(2 x) \sec ^3(x) \, dx\) [432]
3.5.33
\(\int \genfrac {}{}{}{}{\sin ^2(x) (3 \sin ^3(x)-\cos (x) \sin (4 x))}{\cos ^{\genfrac {}{}{}{}{7}{2}}(2 x)} \, dx\) [433]
3.5.34
\(\int (4-5 \sec ^2(x))^{3/2} \, dx\) [434]
3.5.35
\(\int \genfrac {}{}{}{}{1}{(4-5 \sec ^2(x))^{3/2}} \, dx\) [435]
3.5.36
\(\int \genfrac {}{}{}{}{-2 \cot ^2(x)+\sin (x)}{(1+5 \tan ^2(x))^{3/2}} \, dx\) [436]
3.5.37
\(\int \genfrac {}{}{}{}{(-3+\cos (2 x)) \sec ^4(x)}{\sqrt {4-\cot ^2(x)}} \, dx\) [437]
3.5.38
\(\int \genfrac {}{}{}{}{(3+\sin ^2(x)) \tan ^3(x)}{(-2+\cos ^2(x)) (5-4 \sec ^2(x))^{3/2}} \, dx\) [438]
3.5.39
\(\int \genfrac {}{}{}{}{\csc ^2(x) (\sec ^2(x)-3 \tan (x) \sqrt {4 \sec ^2(x)+5 \tan ^2(x)})}{(4 \sec ^2(x)+5 \tan ^2(x))^{3/2}} \, dx\) [439]
3.5.40
\(\int \tan (x) (1+5 \tan ^2(x))^{5/2} \, dx\) [440]
3.5.41
\(\int \genfrac {}{}{}{}{\tan (x)}{(1+5 \tan ^2(x))^{5/2}} \, dx\) [441]
3.5.42
\(\int \genfrac {}{}{}{}{\tan (x)}{\sqrt [3]{a^3+b^3 \tan ^2(x)}} \, dx\) [442]
3.5.43
\(\int \tan (x) (1-7 \tan ^2(x))^{2/3} \, dx\) [443]
3.5.44
\(\int \genfrac {}{}{}{}{\cot (x)}{\sqrt [4]{a^4+b^4 \csc ^2(x)}} \, dx\) [444]
3.5.45
\(\int \genfrac {}{}{}{}{\cot (x)}{\sqrt [4]{a^4-b^4 \csc ^2(x)}} \, dx\) [445]
3.5.46
\(\int \genfrac {}{}{}{}{\sec ^2(x) \tan (x) (\sqrt [3]{1-3 \sec ^2(x)} \sin ^2(x)+3 \tan ^2(x))}{(1-3 \sec ^2(x))^{5/6} (1-\sqrt {1-3 \sec ^2(x)})} \, dx\) [446]
3.5.47
\(\int \genfrac {}{}{}{}{\sec ^2(x) (-\cos (2 x)+2 \tan ^2(x))}{(\tan (x) \tan (2 x))^{3/2}} \, dx\) [447]
3.5.48
\(\int \genfrac {}{}{}{}{\tan (x)}{(a^3-b^3 \cos ^n(x))^{4/3}} \, dx\) [448]
3.5.49
\(\int (1+2 \cos ^9(x))^{5/6} \tan (x) \, dx\) [449]
3.5.50
\(\int \genfrac {}{}{}{}{\cos (x) \sin ^8(x)}{(2-5 \sin ^3(x))^{4/3}} \, dx\) [450]
3.5.51
\(\int \genfrac {}{}{}{}{\sec ^2(x) \tan (x) (1+\sqrt [3]{1-8 \tan ^2(x)})}{(1-8 \tan ^2(x))^{2/3}} \, dx\) [451]
3.5.52
\(\int \genfrac {}{}{}{}{\csc (x) \sec (x) (1+\sqrt [3]{1-8 \tan ^2(x)})}{(1-8 \tan ^2(x))^{2/3}} \, dx\) [452]
3.5.53
\(\int \genfrac {}{}{}{}{(5 \cos ^2(x)-\sqrt {-1+5 \sin ^2(x)}) \tan (x)}{\sqrt [4]{-1+5 \sin ^2(x)} (2+\sqrt {-1+5 \sin ^2(x)})} \, dx\) [453]
3.5.54
\(\int \cos ^3(x) \cos ^{\genfrac {}{}{}{}{2}{3}}(2 x) \sin (x) \, dx\) [454]
3.5.55
\(\int \genfrac {}{}{}{}{\sin ^6(x) \tan (x)}{\cos ^{\genfrac {}{}{}{}{3}{4}}(2 x)} \, dx\) [455]
3.5.56
\(\int \sqrt {\tan (x) \tan (2 x)} \, dx\) [456]
3.5.57
\(\int \sqrt {\cot (2 x) \tan (x)} \, dx\) [457]
3.5.58
\(\int \genfrac {}{}{}{}{1}{x^5 (5+x^2)} \, dx\) [458]
3.5.59
\(\int \genfrac {}{}{}{}{1}{x^6 (5+x^2)} \, dx\) [459]
3.5.60
\(\int \genfrac {}{}{}{}{1}{x (-4+x^2)^4} \, dx\) [460]
3.5.61
\(\int \genfrac {}{}{}{}{1}{x (-2+x^2)^{5/2}} \, dx\) [461]
3.5.62
\(\int \genfrac {}{}{}{}{(-10+x^2)^{5/2}}{x} \, dx\) [462]
3.5.63
\(\int x^{1+2 n} \, dx\) [463]
3.5.64
\(\int \genfrac {}{}{}{}{x^7}{(-5+x^2)^3} \, dx\) [464]
3.5.65
\(\int \genfrac {}{}{}{}{-4 x^3+3 x^5}{(-1+x^2)^5} \, dx\) [465]
3.5.66
\(\int x^3 (1+x^2)^{9/14} \, dx\) [466]
3.5.67
\(\int \genfrac {}{}{}{}{x^5}{(-4+x^2)^{13/6}} \, dx\) [467]
3.5.68
\(\int \genfrac {}{}{}{}{1}{(1+2 x^2)^{5/2}} \, dx\) [468]
3.5.69
\(\int \genfrac {}{}{}{}{1}{(-1-2 x+x^2)^{5/2}} \, dx\) [469]
3.5.70
\(\int \genfrac {}{}{}{}{1}{x^4 (-8+x^2)^{3/2}} \, dx\) [470]
3.5.71
\(\int \genfrac {}{}{}{}{(5+x^2)^2}{x^{13/3}} \, dx\) [471]
3.5.72
\(\int \genfrac {}{}{}{}{1}{x^7 (1+x^2)^3} \, dx\) [472]
3.5.73
\(\int \genfrac {}{}{}{}{(\genfrac {}{}{}{}{2+x^2}{x^2})^{7/9}}{(2+x^2)^{3/2}} \, dx\) [473]
3.5.74
\(\int \genfrac {}{}{}{}{x^4}{(\sqrt {10}-x^2)^{9/2}} \, dx\) [474]
3.5.75
\(\int \genfrac {}{}{}{}{x^2}{(3-x^2)^{3/2}} \, dx\) [475]
3.5.76
\(\int \genfrac {}{}{}{}{(25-x^2)^{3/2}}{x^4} \, dx\) [476]
3.5.77
\(\int \genfrac {}{}{}{}{1}{(1-2 x^2)^{7/2}} \, dx\) [477]
3.5.78
\(\int \genfrac {}{}{}{}{1}{(-7+6 x-x^2)^{5/2}} \, dx\) [478]
3.5.79
\(\int (1-2 x-2 x^2)^3 \, dx\) [479]
3.5.80
\(\int (-1+5 x) (-1-x+x^2)^2 \, dx\) [480]
3.5.81
\(\int \genfrac {}{}{}{}{1+3 x}{(1-8 x+2 x^2)^{5/2}} \, dx\) [481]
3.5.82
\(\int \genfrac {}{}{}{}{-1-8 x+8 x^3}{(1+2 x-4 x^2)^{5/2}} \, dx\) [482]
3.5.83
\(\int x^2 \cos ^5(x) \, dx\) [483]
3.5.84
\(\int x^3 \sin ^3(x) \, dx\) [484]
3.5.85
\(\int x^2 \sin ^6(x) \, dx\) [485]
3.5.86
\(\int x^2 \cos (x) \sin ^2(x) \, dx\) [486]
3.5.87
\(\int x \cos ^2(x) \cot ^2(x) \, dx\) [487]
3.5.88
\(\int x \sec (x) \tan ^3(x) \, dx\) [488]
3.5.89
\(\int x \sec ^2(x) \tan (x) \, dx\) [489]
3.5.90
\(\int x \sin ^2(x) \tan (x) \, dx\) [490]
3.5.91
\(\int x \tan ^3(x) \, dx\) [491]
3.5.92
\(\int \genfrac {}{}{}{}{2 x+\sin (2 x)}{(\cos (x)+x \sin (x))^2} \, dx\) [492]
3.5.93
\(\int \genfrac {}{}{}{}{x^2}{(x \cos (x)-\sin (x))^2} \, dx\) [493]
3.5.94
\(\int a^{m x} b^{n x} \, dx\) [494]
3.5.95
\(\int a^{-x} b^{-x} (a^x-b^x)^2 \, dx\) [495]
3.5.96
\(\int (-e^{-x}+e^x) \, dx\) [496]
3.5.97
\(\int (-e^{-x}+e^x)^2 \, dx\) [497]
3.5.98
\(\int (-e^{-x}+e^x)^3 \, dx\) [498]
3.5.99
\(\int (-e^{-x}+e^x)^4 \, dx\) [499]
3.5.100
\(\int (-e^{-x}+e^x)^n \, dx\) [500]
[
next
] [
prev
] [
prev-tail
] [
front
] [
up
]