Solve ∫ -210824*107^x wrt x

$$\int{ -210824 \times { 107 }^{ x } }d x$$

Evaluate

$$-\frac{210824\times 107^{x}}{\ln(107)}+С$$

Solution Steps

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

$$-210824\int 107^{x}\mathrm{d}x$$

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

$$-210824\times \frac{107^{x}}{\ln(107)}$$

Simplify.

$$-\frac{210824\times 107^{x}}{\ln(107)}$$

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.

$$-\frac{210824\times 107^{x}}{\ln(107)}+С$$

Differentiate w.r.t. x

$$-210824\times 107^{x}$$