Calculus Examples

Evaluate the Integral integral of (x-4x^8)^6 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
Move .
Step 1.18
Move .
Step 1.19
Move parentheses.
Step 1.20
Move parentheses.
Step 1.21
Move .
Step 1.22
Move .
Step 1.23
Move parentheses.
Step 1.24
Move parentheses.
Step 1.25
Move .
Step 1.26
Move parentheses.
Step 1.27
Move parentheses.
Step 1.28
Move parentheses.
Step 1.29
Move parentheses.
Step 1.30
Move .
Step 1.31
Move .
Step 1.32
Move parentheses.
Step 1.33
Move parentheses.
Step 1.34
Move .
Step 1.35
Move parentheses.
Step 1.36
Move parentheses.
Step 1.37
Move parentheses.
Step 1.38
Move parentheses.
Step 1.39
Move .
Step 1.40
Move parentheses.
Step 1.41
Move parentheses.
Step 1.42
Move parentheses.
Step 1.43
Move parentheses.
Step 1.44
Move parentheses.
Step 1.45
Move .
Step 1.46
Move parentheses.
Step 1.47
Move .
Step 1.48
Move parentheses.
Step 1.49
Move parentheses.
Step 1.50
Move .
Step 1.51
Move parentheses.
Step 1.52
Move parentheses.
Step 1.53
Move parentheses.
Step 1.54
Move parentheses.
Step 1.55
Move .
Step 1.56
Move parentheses.
Step 1.57
Move parentheses.
Step 1.58
Move parentheses.
Step 1.59
Move parentheses.
Step 1.60
Move parentheses.
Step 1.61
Move .
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 .
Step 1.70
Move parentheses.
Step 1.71
Move parentheses.
Step 1.72
Move .
Step 1.73
Move parentheses.
Step 1.74
Move parentheses.
Step 1.75
Move .
Step 1.76
Move parentheses.
Step 1.77
Move parentheses.
Step 1.78
Move parentheses.
Step 1.79
Move parentheses.
Step 1.80
Move .
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 .
Step 1.87
Move parentheses.
Step 1.88
Move parentheses.
Step 1.89
Move parentheses.
Step 1.90
Move parentheses.
Step 1.91
Move parentheses.
Step 1.92
Move parentheses.
Step 1.93
Move parentheses.
Step 1.94
Move .
Step 1.95
Move parentheses.
Step 1.96
Move parentheses.
Step 1.97
Multiply by .
Step 1.98
Use the power rule to combine exponents.
Step 1.99
Add and .
Step 1.100
Multiply by .
Step 1.101
Multiply by .
Step 1.102
Use the power rule to combine exponents.
Step 1.103
Add and .
Step 1.104
Use the power rule to combine exponents.
Step 1.105
Add and .
Step 1.106
Multiply by .
Step 1.107
Multiply by .
Step 1.108
Multiply by .
Step 1.109
Use the power rule to combine exponents.
Step 1.110
Add and .
Step 1.111
Use the power rule to combine exponents.
Step 1.112
Add and .
Step 1.113
Use the power rule to combine exponents.
Step 1.114
Add and .
Step 1.115
Multiply by .
Step 1.116
Multiply by .
Step 1.117
Multiply by .
Step 1.118
Multiply by .
Step 1.119
Use the power rule to combine exponents.
Step 1.120
Add and .
Step 1.121
Use the power rule to combine exponents.
Step 1.122
Add and .
Step 1.123
Use the power rule to combine exponents.
Step 1.124
Add and .
Step 1.125
Use the power rule to combine exponents.
Step 1.126
Add and .
Step 1.127
Multiply by .
Step 1.128
Multiply by .
Step 1.129
Multiply by .
Step 1.130
Multiply by .
Step 1.131
Multiply by .
Step 1.132
Raise to the power of .
Step 1.133
Use the power rule to combine exponents.
Step 1.134
Add and .
Step 1.135
Use the power rule to combine exponents.
Step 1.136
Add and .
Step 1.137
Use the power rule to combine exponents.
Step 1.138
Add and .
Step 1.139
Use the power rule to combine exponents.
Step 1.140
Add and .
Step 1.141
Use the power rule to combine exponents.
Step 1.142
Add and .
Step 1.143
Multiply by .
Step 1.144
Multiply by .
Step 1.145
Multiply by .
Step 1.146
Multiply by .
Step 1.147
Multiply by .
Step 1.148
Use the power rule to combine exponents.
Step 1.149
Add and .
Step 1.150
Use the power rule to combine exponents.
Step 1.151
Add and .
Step 1.152
Use the power rule to combine exponents.
Step 1.153
Add and .
Step 1.154
Use the power rule to combine exponents.
Step 1.155
Add and .
Step 1.156
Use the power rule to combine exponents.
Step 1.157
Add and .
Step 1.158
Reorder and .
Step 1.159
Move .
Step 1.160
Reorder and .
Step 1.161
Move .
Step 1.162
Move .
Step 1.163
Reorder and .
Step 1.164
Move .
Step 1.165
Move .
Step 1.166
Move .
Step 1.167
Reorder and .
Step 1.168
Move .
Step 1.169
Move .
Step 1.170
Move .
Step 1.171
Move .
Step 1.172
Reorder and .
Step 1.173
Move .
Step 1.174
Move .
Step 1.175
Move .
Step 1.176
Move .
Step 1.177
Move .
Step 1.178
Reorder and .
Step 2
Split the single integral into multiple integrals.
Step 3
Since is constant with respect to , move out of the integral.
Step 4
By the Power Rule, the integral of with respect to is .
Step 5
Since is constant with respect to , move out of the integral.
Step 6
By the Power Rule, the integral of with respect to is .
Step 7
Since is constant with respect to , move out of the integral.
Step 8
By the Power Rule, the integral of with respect to is .
Step 9
Since is constant with respect to , move out of the integral.
Step 10
By the Power Rule, the integral of with respect to is .
Step 11
Since is constant with respect to , move out of the integral.
Step 12
By the Power Rule, the integral of with respect to is .
Step 13
Since is constant with respect to , move out of the integral.
Step 14
By the Power Rule, the integral of with respect to is .
Step 15
By the Power Rule, the integral of with respect to is .
Step 16
Simplify.
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Step 16.1
Simplify.
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Step 16.1.1
Combine and .
Step 16.1.2
Combine and .
Step 16.1.3
Combine and .
Step 16.1.4
Combine and .
Step 16.1.5
Combine and .
Step 16.1.6
Combine and .
Step 16.2
Simplify.
Step 17
Reorder terms.