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Question 1 of 5
Find the integral
∫32x−6dx
Incorrect
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First, form a fraction to balance the equation.
∫f′(x)f(x) |
= |
∫32x−6 |
|
|
= |
32 |
Differentiate the denominator |
Use 32 as a constant to balance the integral.
∫f′(x)f(x)dx |
= |
loge[f(x)]+c |
|
∫32x−6dx |
= |
32ln[2x−6]+c |
Substitute known values |
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Question 2 of 5
Find the integral
∫x22x3+4dx
Incorrect
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First, form a fraction to balance the equation.
∫f′(x)f(x) |
= |
∫x22x3+4 |
|
|
= |
x26x2 |
Differentiate the denominator |
|
|
= |
16 |
x2x2=1 |
Use 16 as a constant to balance the integral.
16∫f′(x)f(x)dx |
= |
16loge[f(x)]+c |
|
16∫6x22x3+4dx |
= |
16ln[2x3+4]+c |
Substitute known values |
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Question 3 of 5
Find the integral
∫x52x6+3dx
Incorrect
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Progress: 0%
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First, form a fraction to balance the equation.
∫f′(x)f(x) |
= |
∫x52x6+3 |
|
|
= |
x512x5 |
Differentiate the denominator |
|
|
= |
112 |
x5x5=1 |
Use 112 as a constant to balance the integral.
f(x) |
= |
2x6+3 |
f′(x) |
= |
12x5 |
112∫f′(x)f(x)dx |
= |
112loge[f(x)]+c |
|
112∫12x52x6+3dx |
= |
112ln[2x6+3]+c |
Substitute known values |
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Question 4 of 5
Find the integral
∫x(x+3)(x−3)dx
Incorrect
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Progress: 0%
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First, form a fraction to balance the equation.
∫f′(x)f(x) |
= |
∫x(x+3)(x−3) |
|
|
= |
xx2−9 |
Expand |
|
|
= |
x2x |
Differentiate the denominator |
|
|
= |
12 |
xx=1 |
Use 12 as a constant to balance the integral.
12∫f′(x)f(x)dx |
= |
12loge[f(x)]+c |
|
12∫2xx2−9dx |
= |
12ln[x2−9]+c |
Substitute known values |
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Question 5 of 5
Find the integral
∫x+3x2+6x−1dx
Incorrect
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First, form a fraction to balance the equation.
∫f′(x)f(x) |
= |
∫x+3x2+6x−1 |
|
|
= |
x+32x+6 |
Differentiate the denominator |
|
|
= |
x+32(x+3) |
Factorize |
|
|
= |
12 |
x+3x+3=1 |
Use 12 as a constant to balance the integral.
f(x) |
= |
x2+6x-1 |
f′(x) |
= |
2x+6 |
12∫f′(x)f(x)dx |
= |
12loge[f(x)]+c |
|
12∫2x+6x2+6x−1dx |
= |
12ln[x2+6x−1]+c |
Substitute known values |