Solve ∫ 10sins+7cossds

$$\int 10 \sin s + 7 \cos s d s$$

Evaluate

$$7\sin(s)-10\cos(s)+С$$

Solution Steps

Integrate the sum term by term.

$$\int 10\sin(s)\mathrm{d}s+\int 7\cos(s)\mathrm{d}s$$

Factor out the constant in each of the terms.

$$10\int \sin(s)\mathrm{d}s+7\int \cos(s)\mathrm{d}s$$

Use \int \sin(s)\mathrm{d}s=-\cos(s) from the table of common integrals to obtain the result. Multiply 10 times -\cos(s).

$$-10\cos(s)+7\int \cos(s)\mathrm{d}s$$

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

$$-10\cos(s)+7\sin(s)$$

If F\left(s\right) is an antiderivative of f\left(s\right), then the set of all antiderivatives of f\left(s\right) is given by F\left(s\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$-10\cos(s)+7\sin(s)+С$$

Differentiate w.r.t. s

$$7\cos(s)+10\sin(s)$$