Solve ∫ (cosx+2^x) wrt x=

$$\int ( \cos x + 2 ^ { x } ) d x =$$

Evaluate

$$\frac{2^{x}}{\ln(2)}+\sin(x)+С$$

Solution Steps

Integrate the sum term by term.

$$\int \cos(x)\mathrm{d}x+\int 2^{x}\mathrm{d}x$$

Use \int \cos(x)\mathrm{d}x=\sin(x) from the table of common integrals to obtain the result.

$$\sin(x)+\int 2^{x}\mathrm{d}x$$

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

$$\sin(x)+\frac{2^{x}}{\ln(2)}$$

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.

$$\sin(x)+\frac{2^{x}}{\ln(2)}+С$$

Differentiate w.r.t. x

$$2^{x}+\cos(x)$$