Solve ∫ 832^2-150^2/83^2-160

$$\int \frac { 832 ^ { 2 } - 150 ^ { 2 } } { 83 ^ { 2 } - 160 }$$

Evaluate

$$\frac{669724x}{6729}+С$$

Solution Steps

Calculate 832 to the power of 2 and get 692224.

$$\int \frac{692224-150^{2}}{83^{2}-160}\mathrm{d}x$$

Calculate 150 to the power of 2 and get 22500.

$$\int \frac{692224-22500}{83^{2}-160}\mathrm{d}x$$

Subtract 22500 from 692224 to get 669724.

$$\int \frac{669724}{83^{2}-160}\mathrm{d}x$$

Calculate 83 to the power of 2 and get 6889.

$$\int \frac{669724}{6889-160}\mathrm{d}x$$

Subtract 160 from 6889 to get 6729.

$$\int \frac{669724}{6729}\mathrm{d}x$$

Find the integral of \frac{669724}{6729} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\frac{669724x}{6729}$$

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.

$$\frac{669724x}{6729}+С$$

Differentiate w.r.t. x

$$\frac{669724}{6729} = 99\frac{3553}{6729} = 99.52801307772329$$