Solve ∫ sqrt{3^6*5^2}

$$\int \sqrt { 3 ^ { 6 } \cdot 5 ^ { 2 } }$$

Evaluate

$$135x+С$$

Solution Steps

Calculate 3 to the power of 6 and get 729.

$$\int \sqrt{729\times 5^{2}}\mathrm{d}x$$

Calculate 5 to the power of 2 and get 25.

$$\int \sqrt{729\times 25}\mathrm{d}x$$

Multiply 729 and 25 to get 18225.

$$\int \sqrt{18225}\mathrm{d}x$$

Calculate the square root of 18225 and get 135.

$$\int 135\mathrm{d}x$$

Find the integral of 135 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$135x$$

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.

$$135x+С$$

Differentiate w.r.t. x

$$135$$