Solve ∫ 3^x-4(3^x)

$$\int 3 ^ { x } - 4 ( 3 ^ { x } )$$

Evaluate

$$-\frac{3^{x+1}}{\ln(3)}+С$$

Solution Steps

Integrate the sum term by term.

$$\int 3^{x}\mathrm{d}x+\int -4\times 3^{x}\mathrm{d}x$$

Factor out the constant in each of the terms.

$$\int 3^{x}\mathrm{d}x-4\int 3^{x}\mathrm{d}x$$

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

$$\frac{3^{x}}{\ln(3)}-4\int 3^{x}\mathrm{d}x$$

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

$$\frac{3^{x}}{\ln(3)}-4\times \frac{3^{x}}{\ln(3)}$$

Simplify.

$$-\frac{3\times 3^{x}}{\ln(3)}$$

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.

$$-\frac{3\times 3^{x}}{\ln(3)}+С$$

Differentiate w.r.t. x

$$-3^{x+1}$$