82

77.

79.

81.

82.

84.

86.

87.

88.

89.

90.

91.

92.

93.

94.

95.

96.

97. 99.

101.

103.

105.

107.

109.

I 10.

111.

112.

114.

|(.x⁴ — 4a;)³ + C; x⁴ - 4x — t iarctgx² + C; x² = t

78.

80.

fe(a;² + 3)-⁵ + C

10

-i(x³ + 5)--³ + C

2(l+x⁵) ['

i ,    3___1_ ,    1

^{1 +} 2(l+x²)    (1 + z²)²    (l+Z²)³

+ C; 1 + ar

83.

9(a?H-l)» ” S(x+l)^s

| arcsin y³ + C; y³ = t e^x - arctge²-' + C; e^x = t

xarctgx — | ln(l + x²) — |(arctg.x)² + (7; arctg.x = t.

x — \/l — x² arcsin x + C; arcsin x = t

85. \e^x\x² - l) + C

j |x⁴ arcsin 1 + sgn(x)^x-j² y/x² — lj + C; u = arcsin 1, v' = x³

rr(arccosx)² — 2\/\~^x² arccosx — 2x + C; arccos x = t xarctgi/x + arctgVx -    + (7; u = arctg^/ic, u⁷ = 1

~ j arcsin x + C

ln

\x³ arcsinx + §x²\/l - x² +    - x² + C

^x²arctgx² ~ \ ln(l + x⁴) + C\ x² = t x — e~ ^,rarctge^x — | ln(l + e^2x) + (7; e^x = t [ln(lnx) — 1] lnx + C\ Ina; = i

j ln |3x + 5j + C iarctgf + C arctg(x + 1) + C

ln

x — 3

x — 2 x — J

+ c

ln Pr¹ +C

.1- I

+ c

98. -i(2x-3)^^s + C 100. | ln(x² + 9) + |arctg| + C

102 • -^3+C

104. ln

2z+l

x-\-l

106. 1 ln

x-2

x~\~‘2

+ c + c

ln|(.r - 3)(x + 2)²| + C ln(x² - x + 1) + v/3arctg2^1 + C

ln \x + 1| + | ln(x² + x + 1) + 73^arctg^^ + C

108. i ln ^^3|y^r‘ + C

lin

ln

X+1

X i

Aarftgz + C

+ 75^arctg^ + ^c

113. 2arctgx + ln |x| + C 115. ^arctg^ - larctgf +C

117.

118.

119.

120. 122.

124.

125.

iln|(o; + 2)⁹(x-2)⁷| + ₅^₊C

ln [a;²|a: + 2|] +    + C

~7+T + ł^hl [(2 + x²)\x + 1|] - ^arctg^j + C

5 ln

3j;+5

+ farctgz + C

•/ x^,2-f-l    2(a;²-j-l)

k ln + 7J^arctg^ + ^c

V3

1__X2 __{2x + ln}i0L₊c

|:r⁵ - 2x³ + 4x - ^®arctgy^|a: + C — i cos 3x + C

121. |x² — \ ln(a:² + 1) + C

¹²³- z² - 37 ~ ^73^arctS^ + C

126. 10 sin f +C

— | cos 2x — jg cos 8x + C

128.

sin 5x + 5 sin x + C

127.

129 131.

133.

135. 3- sin'⁵ x

137.

138.    |(x — \ sin4:r) + C

139.    |t,g².x + ln | cosx| + C;. f tg³xdx = f tgx^±r—dx - f tgxdx

140.

142.

^ sin(6.T+2) +1 sin(2x +4) +C itg4x — x + C

3 sin³ x

+ c

- | sin⁵ x + C

130. \x + \ sin 2x + C 132. — |(cosx)2 + C 134. cos x — 2arctg(cos x) + C 136. i cos³ X - cos X + C

| (x — sin x cos x — | sin³ x cos x) + C; sin² x = ^{1 c}£^s 2x

~x - sin 4x + ^ sin³ 2x + C

141. -arctg (2tg|) + C\ tg| = t

t ln

144.

146.

147.

148.

2+tg j

arctg

f ln

2-tgf

l+5tgf

2

tgf-T

+ C

+ <7; tgf = t

+ C

tgf+2

\/2arctg(\/2tgx) — x + C; tgx = t ijarctg(sin² x) + C; sin² x = t

143. 4= arctg^i + C

7S

145. i ln

149. -i

^5 (1+sin -r)

(3+sin x)(1 —sin x)

+ c

l+j-

~) +C;    = t²

150. ln jl — \/l — x²\ — ln \x\ — arcsinx + C

151-t (^y+c;    =t³

152.    2y/x - 3\/x I 6tyx 6ln(l + tfx) + C; x = t°

153.    6({/x nrcl.g</x) -ł ( x /"    154.6- \xjfx + C\ x = t

A