Calculus Examples

Evaluate the Integral integral of (x^4+9)^8 with respect to x
Step 1
Expand .
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Step 1.1
Use the Binomial Theorem.
Step 1.2
Rewrite the exponentiation as a product.
Step 1.3
Rewrite the exponentiation as a product.
Step 1.4
Rewrite the exponentiation as a product.
Step 1.5
Rewrite the exponentiation as a product.
Step 1.6
Rewrite the exponentiation as a product.
Step 1.7
Rewrite the exponentiation as a product.
Step 1.8
Rewrite the exponentiation as a product.
Step 1.9
Rewrite the exponentiation as a product.
Step 1.10
Rewrite the exponentiation as a product.
Step 1.11
Rewrite the exponentiation as a product.
Step 1.12
Rewrite the exponentiation as a product.
Step 1.13
Rewrite the exponentiation as a product.
Step 1.14
Rewrite the exponentiation as a product.
Step 1.15
Rewrite the exponentiation as a product.
Step 1.16
Rewrite the exponentiation as a product.
Step 1.17
Rewrite the exponentiation as a product.
Step 1.18
Rewrite the exponentiation as a product.
Step 1.19
Rewrite the exponentiation as a product.
Step 1.20
Rewrite the exponentiation as a product.
Step 1.21
Rewrite the exponentiation as a product.
Step 1.22
Rewrite the exponentiation as a product.
Step 1.23
Rewrite the exponentiation as a product.
Step 1.24
Rewrite the exponentiation as a product.
Step 1.25
Rewrite the exponentiation as a product.
Step 1.26
Rewrite the exponentiation as a product.
Step 1.27
Rewrite the exponentiation as a product.
Step 1.28
Rewrite the exponentiation as a product.
Step 1.29
Rewrite the exponentiation as a product.
Step 1.30
Rewrite the exponentiation as a product.
Step 1.31
Rewrite the exponentiation as a product.
Step 1.32
Rewrite the exponentiation as a product.
Step 1.33
Rewrite the exponentiation as a product.
Step 1.34
Rewrite the exponentiation as a product.
Step 1.35
Rewrite the exponentiation as a product.
Step 1.36
Rewrite the exponentiation as a product.
Step 1.37
Rewrite the exponentiation as a product.
Step 1.38
Rewrite the exponentiation as a product.
Step 1.39
Rewrite the exponentiation as a product.
Step 1.40
Rewrite the exponentiation as a product.
Step 1.41
Rewrite the exponentiation as a product.
Step 1.42
Rewrite the exponentiation as a product.
Step 1.43
Rewrite the exponentiation as a product.
Step 1.44
Rewrite the exponentiation as a product.
Step 1.45
Rewrite the exponentiation as a product.
Step 1.46
Rewrite the exponentiation as a product.
Step 1.47
Rewrite the exponentiation as a product.
Step 1.48
Rewrite the exponentiation as a product.
Step 1.49
Rewrite the exponentiation as a product.
Step 1.50
Rewrite the exponentiation as a product.
Step 1.51
Rewrite the exponentiation as a product.
Step 1.52
Rewrite the exponentiation as a product.
Step 1.53
Rewrite the exponentiation as a product.
Step 1.54
Rewrite the exponentiation as a product.
Step 1.55
Rewrite the exponentiation as a product.
Step 1.56
Rewrite the exponentiation as a product.
Step 1.57
Rewrite the exponentiation as a product.
Step 1.58
Move parentheses.
Step 1.59
Move parentheses.
Step 1.60
Move parentheses.
Step 1.61
Move parentheses.
Step 1.62
Move parentheses.
Step 1.63
Move parentheses.
Step 1.64
Move parentheses.
Step 1.65
Move parentheses.
Step 1.66
Move parentheses.
Step 1.67
Move parentheses.
Step 1.68
Move parentheses.
Step 1.69
Move parentheses.
Step 1.70
Move parentheses.
Step 1.71
Move parentheses.
Step 1.72
Move parentheses.
Step 1.73
Move parentheses.
Step 1.74
Move parentheses.
Step 1.75
Move parentheses.
Step 1.76
Move parentheses.
Step 1.77
Move parentheses.
Step 1.78
Move parentheses.
Step 1.79
Move parentheses.
Step 1.80
Move parentheses.
Step 1.81
Move parentheses.
Step 1.82
Move parentheses.
Step 1.83
Move parentheses.
Step 1.84
Move parentheses.
Step 1.85
Move parentheses.
Step 1.86
Move parentheses.
Step 1.87
Move parentheses.
Step 1.88
Move .
Step 1.89
Move .
Step 1.90
Move .
Step 1.91
Move .
Step 1.92
Move .
Step 1.93
Move .
Step 1.94
Move .
Step 1.95
Move parentheses.
Step 1.96
Move parentheses.
Step 1.97
Move parentheses.
Step 1.98
Move parentheses.
Step 1.99
Move parentheses.
Step 1.100
Move parentheses.
Step 1.101
Move parentheses.
Step 1.102
Move parentheses.
Step 1.103
Move parentheses.
Step 1.104
Move parentheses.
Step 1.105
Move .
Step 1.106
Move .
Step 1.107
Move .
Step 1.108
Move .
Step 1.109
Move .
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Move .
Step 1.111
Move parentheses.
Step 1.112
Move parentheses.
Step 1.113
Move parentheses.
Step 1.114
Move parentheses.
Step 1.115
Move parentheses.
Step 1.116
Move parentheses.
Step 1.117
Move parentheses.
Step 1.118
Move .
Step 1.119
Move .
Step 1.120
Move .
Step 1.121
Move .
Step 1.122
Move .
Step 1.123
Move parentheses.
Step 1.124
Move parentheses.
Step 1.125
Move parentheses.
Step 1.126
Move parentheses.
Step 1.127
Move parentheses.
Step 1.128
Move .
Step 1.129
Move .
Step 1.130
Move .
Step 1.131
Move .
Step 1.132
Move parentheses.
Step 1.133
Move parentheses.
Step 1.134
Move parentheses.
Step 1.135
Move parentheses.
Step 1.136
Move parentheses.
Step 1.137
Move parentheses.
Step 1.138
Move .
Step 1.139
Move .
Step 1.140
Move .
Step 1.141
Move parentheses.
Step 1.142
Move parentheses.
Step 1.143
Move parentheses.
Step 1.144
Move parentheses.
Step 1.145
Move parentheses.
Step 1.146
Move parentheses.
Step 1.147
Move parentheses.
Step 1.148
Move parentheses.
Step 1.149
Move parentheses.
Step 1.150
Move .
Step 1.151
Move .
Step 1.152
Move parentheses.
Step 1.153
Move parentheses.
Step 1.154
Move parentheses.
Step 1.155
Move parentheses.
Step 1.156
Move parentheses.
Step 1.157
Move parentheses.
Step 1.158
Move parentheses.
Step 1.159
Move parentheses.
Step 1.160
Move parentheses.
Step 1.161
Move parentheses.
Step 1.162
Move parentheses.
Step 1.163
Move parentheses.
Step 1.164
Move parentheses.
Step 1.165
Move parentheses.
Step 1.166
Move .
Step 1.167
Move parentheses.
Step 1.168
Move parentheses.
Step 1.169
Move parentheses.
Step 1.170
Move parentheses.
Step 1.171
Move parentheses.
Step 1.172
Move parentheses.
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Move parentheses.
Step 1.174
Move parentheses.
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Move parentheses.
Step 1.176
Move parentheses.
Step 1.177
Move parentheses.
Step 1.178
Move parentheses.
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Move parentheses.
Step 1.180
Move parentheses.
Step 1.181
Move parentheses.
Step 1.182
Move parentheses.
Step 1.183
Move parentheses.
Step 1.184
Move parentheses.
Step 1.185
Move parentheses.
Step 1.186
Use the power rule to combine exponents.
Step 1.187
Add and .
Step 1.188
Use the power rule to combine exponents.
Step 1.189
Add and .
Step 1.190
Use the power rule to combine exponents.
Step 1.191
Add and .
Step 1.192
Use the power rule to combine exponents.
Step 1.193
Add and .
Step 1.194
Use the power rule to combine exponents.
Step 1.195
Add and .
Step 1.196
Use the power rule to combine exponents.
Step 1.197
Add and .
Step 1.198
Use the power rule to combine exponents.
Step 1.199
Add and .
Step 1.200
Multiply by .
Step 1.201
Use the power rule to combine exponents.
Step 1.202
Add and .
Step 1.203
Use the power rule to combine exponents.
Step 1.204
Add and .
Step 1.205
Use the power rule to combine exponents.
Step 1.206
Add and .
Step 1.207
Use the power rule to combine exponents.
Step 1.208
Add and .
Step 1.209
Use the power rule to combine exponents.
Step 1.210
Add and .
Step 1.211
Use the power rule to combine exponents.
Step 1.212
Add and .
Step 1.213
Multiply by .
Step 1.214
Multiply by .
Step 1.215
Use the power rule to combine exponents.
Step 1.216
Add and .
Step 1.217
Use the power rule to combine exponents.
Step 1.218
Add and .
Step 1.219
Use the power rule to combine exponents.
Step 1.220
Add and .
Step 1.221
Use the power rule to combine exponents.
Step 1.222
Add and .
Step 1.223
Use the power rule to combine exponents.
Step 1.224
Add and .
Step 1.225
Multiply by .
Step 1.226
Multiply by .
Step 1.227
Multiply by .
Step 1.228
Use the power rule to combine exponents.
Step 1.229
Add and .
Step 1.230
Use the power rule to combine exponents.
Step 1.231
Add and .
Step 1.232
Use the power rule to combine exponents.
Step 1.233
Add and .
Step 1.234
Use the power rule to combine exponents.
Step 1.235
Add and .
Step 1.236
Multiply by .
Step 1.237
Multiply by .
Step 1.238
Multiply by .
Step 1.239
Multiply by .
Step 1.240
Use the power rule to combine exponents.
Step 1.241
Add and .
Step 1.242
Use the power rule to combine exponents.
Step 1.243
Add and .
Step 1.244
Use the power rule to combine exponents.
Step 1.245
Add and .
Step 1.246
Multiply by .
Step 1.247
Multiply by .
Step 1.248
Multiply by .
Step 1.249
Multiply by .
Step 1.250
Multiply by .
Step 1.251
Use the power rule to combine exponents.
Step 1.252
Add and .
Step 1.253
Use the power rule to combine exponents.
Step 1.254
Add and .
Step 1.255
Multiply by .
Step 1.256
Multiply by .
Step 1.257
Multiply by .
Step 1.258
Multiply by .
Step 1.259
Multiply by .
Step 1.260
Multiply by .
Step 1.261
Use the power rule to combine exponents.
Step 1.262
Add and .
Step 1.263
Multiply by .
Step 1.264
Multiply by .
Step 1.265
Multiply by .
Step 1.266
Multiply by .
Step 1.267
Multiply by .
Step 1.268
Multiply by .
Step 1.269
Multiply by .
Step 1.270
Multiply by .
Step 1.271
Multiply by .
Step 1.272
Multiply by .
Step 1.273
Multiply by .
Step 1.274
Multiply by .
Step 1.275
Multiply by .
Step 1.276
Multiply by .
Step 2
Split the single integral into multiple integrals.
Step 3
By the Power Rule, the integral of with respect to is .
Step 4
Since is constant with respect to , move out of the integral.
Step 5
By the Power Rule, the integral of with respect to is .
Step 6
Since is constant with respect to , move out of the integral.
Step 7
By the Power Rule, the integral of with respect to is .
Step 8
Since is constant with respect to , move out of the integral.
Step 9
By the Power Rule, the integral of with respect to is .
Step 10
Since is constant with respect to , move out of the integral.
Step 11
By the Power Rule, the integral of with respect to is .
Step 12
Since is constant with respect to , move out of the integral.
Step 13
By the Power Rule, the integral of with respect to is .
Step 14
Since is constant with respect to , move out of the integral.
Step 15
By the Power Rule, the integral of with respect to is .
Step 16
Since is constant with respect to , move out of the integral.
Step 17
By the Power Rule, the integral of with respect to is .
Step 18
Apply the constant rule.
Step 19
Simplify.
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Step 19.1
Simplify.
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Step 19.1.1
Combine and .
Step 19.1.2
Combine and .
Step 19.1.3
Combine and .
Step 19.1.4
Combine and .
Step 19.1.5
Combine and .
Step 19.1.6
Combine and .
Step 19.1.7
Combine and .
Step 19.2
Simplify.
Step 19.3
Reorder terms.