Verify the Integration Formula

question 71

True/False

Verify the integration formula.
- $$\int x \operatorname { csch } ^ { - 1 } x d x = \frac { x ^ { 2 } } { 2 } \operatorname { csch } ^ { - 1 } x + \frac { 1 } { 2 } \sqrt { 1 + x ^ { 2 } } + C$$

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Definitions:

MPS

The marginal propensity to save, which is the proportion of an increase in income that is saved rather than spent on consumption.

Disposable Income

Funds at households' discretion for savings and spending pursuits after the deduction of income taxes.

Autonomous Consumption

The minimum level of consumption that would still occur even if a consumer had no income, based on basic needs and obligations.

MPS

Marginal Propensity to Save, which is the fraction of an increase in income that is not spent on an increase in consumption.