Solve ∫ cossqrt{x}*sqrtx^-1 wrt x

$$\int \cos \sqrt { x } \times \sqrt { x } ^ { - 1 } d x$$

Evaluate

$$\cos(1)x+С$$

Solution Steps

Multiply \sqrt{x} and \left(\sqrt{x}\right)^{-1} to get 1.

$$\int \cos(1)\mathrm{d}x$$

Find the integral of \cos(1) using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\cos(1)x$$

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.

$$\cos(1)x+С$$

Differentiate w.r.t. x

$$\cos(1)$$