Solve ∫ 10xsqrt{10}*sqrt{10}

$$\int 10 x \sqrt { 10 } \times \sqrt { 10 }$$

Evaluate

$$50x^{2}+С$$

Solution Steps

Multiply \sqrt{10} and \sqrt{10} to get 10.

$$\int 10x\times 10\mathrm{d}x$$

Multiply 10 and 10 to get 100.

$$\int 100x\mathrm{d}x$$

Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.

$$100\int x\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x\mathrm{d}x with \frac{x^{2}}{2}. Multiply 100 times \frac{x^{2}}{2}.

$$50x^{2}$$

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.

$$50x^{2}+С$$

Differentiate w.r.t. x

$$100x$$