Solve ∫ -2.10824(1.07^x) wrt x

$$\int{ -2.10824( { 1.07 }^{ x } ) }d x$$

Evaluate

$$-\frac{26353\times 1.07^{x}}{12500\ln(1.07)}+С$$

Solution Steps

Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.

$$-\frac{26353\int 1.07^{x}\mathrm{d}x}{12500}$$

Use \int p^{q}\mathrm{d}q=\frac{p^{q}}{\ln(p)} from the table of common integrals to obtain the result.

$$\frac{1.07^{x}}{\ln(1.07)}$$

Simplify.

$$-\frac{26353\times \frac{1.07^{x}}{\ln(\frac{107}{100})}}{12500}$$

Simplify.

$$-\frac{26353\times 1.07^{x}}{12500\ln(\frac{107}{100})}$$

If F\left(x\right) is an antiderivative of f\left(x\right), then the set of all antiderivatives of f\left(x\right) is given by F\left(x\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$-\frac{26353\times 1.07^{x}}{12500\ln(\frac{107}{100})}+С$$

Differentiate w.r.t. x

$$-\frac{26353\times 1.07^{x}}{12500}$$