Solve ∫ 3^2+4^2+5^2

$$\int 3 ^ { 2 } + 4 ^ { 2 } + 5 ^ { 2 }$$

Evaluate

$$50x+С$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\int 9+4^{2}+5^{2}\mathrm{d}x$$

Calculate 4 to the power of 2 and get 16.

$$\int 9+16+5^{2}\mathrm{d}x$$

Add 9 and 16 to get 25.

$$\int 25+5^{2}\mathrm{d}x$$

Calculate 5 to the power of 2 and get 25.

$$\int 25+25\mathrm{d}x$$

Add 25 and 25 to get 50.

$$\int 50\mathrm{d}x$$

Find the integral of 50 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$50x$$

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.

$$50x+С$$

Differentiate w.r.t. x

$$50$$