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Question 1 of 5
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Substitute the components into the formula
∫5xdx |
= |
5∫1xdx |
Take out the constant 5 |
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|
= |
5lnx+c |
Substitute known values |
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Question 2 of 5
Find the integral
∫3x2+4x−6xdx
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Substitute the components into the formula
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∫3x2+4x−6xdx |
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|
= |
3x33+4x22−6∫1xdx |
Take out the constants and integrate |
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|
= |
x3+2x2−6lnx+c |
Simplify |
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Question 3 of 5
Find the integral
∫dxx+5dx
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First, form a fraction to balance the equation.
∫f′(x)f(x) |
= |
∫1x+5 |
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|
= |
11 |
Differentiate the denominator |
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|
= |
1 |
Since it satisfies f′(x)f(x), the equation is already balanced.
Substitute the components to the formula
∫f′(x)f(x)dx |
= |
loge[f(x)]+c |
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∫dxx+5dx |
= |
ln[x+5]+c |
Substitute known values |
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Question 4 of 5
Find the integral
∫2xx2+1dx
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First, form a fraction to balance the equation.
∫f′(x)f(x) |
= |
∫2xx2+1 |
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|
= |
2x2x |
Differentiate the denominator |
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|
= |
1 |
Since it satisfies f′(x)f(x), the equation is already balanced.
Substitute the components to the formula
∫f′(x)f(x)dx |
= |
loge[f(x)]+c |
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∫2xx2+1dx |
= |
ln[x2+1]+c |
Substitute known values |
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Question 5 of 5
Find the integral
∫14x−7dx
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First, form a fraction to balance the equation.
∫f′(x)f(x) |
= |
∫14x−7 |
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|
= |
14 |
Differentiate the denominator |
Use 14 as a constant to balance the integral.
14∫f′(x)f(x)dx |
= |
14loge[f(x)]+c |
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14∫44x−7dx |
= |
14∫44x−7 |
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= |
14ln[4x−7]+c |
Substitute known values |