Solve ∫ 10^x*ln10 wrt x

$$\int 10 ^ { x } \cdot \ln 10 d x$$

Evaluate

$$10^{x}+С$$

Solution Steps

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

$$\log_{e}\left(10\right)\int 10^{x}\mathrm{d}x$$

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

$$\log_{e}\left(10\right)\times \frac{10^{x}}{\ln(10)}$$

Simplify.

$$10^{x}$$

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.

$$10^{x}+С$$

Differentiate w.r.t. x

$$\ln(10)\times 10^{x}$$