Solve ∫ (sinx+2cosx) wrt x=

$$\int ( \sin x + 2 \cos x ) d x =$$

Evaluate

$$2\sin(x)-\cos(x)+С$$

Solution Steps

Integrate the sum term by term.

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

Factor out the constant in each of the terms.

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

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

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

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

$$-\cos(x)+2\sin(x)$$

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.

$$-\cos(x)+2\sin(x)+С$$

Differentiate w.r.t. x

$$\sin(x)+2\cos(x)$$