Solve ∫ 84/5*21/2

$$\int 8 \frac { 4 } { 5 } \times 2 \frac { 1 } { 2 }$$

Evaluate

$$22x+С$$

Solution Steps

Multiply 8 and 5 to get 40.

$$\int \frac{40+4}{5}\times \frac{2\times 2+1}{2}\mathrm{d}x$$

Add 40 and 4 to get 44.

$$\int \frac{44}{5}\times \frac{2\times 2+1}{2}\mathrm{d}x$$

Multiply 2 and 2 to get 4.

$$\int \frac{44}{5}\times \frac{4+1}{2}\mathrm{d}x$$

Add 4 and 1 to get 5.

$$\int \frac{44}{5}\times \frac{5}{2}\mathrm{d}x$$

Multiply \frac{44}{5} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\int \frac{44\times 5}{5\times 2}\mathrm{d}x$$

Cancel out 5 in both numerator and denominator.

$$\int \frac{44}{2}\mathrm{d}x$$

Divide 44 by 2 to get 22.

$$\int 22\mathrm{d}x$$

Find the integral of 22 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$22x$$

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.

$$22x+С$$

Differentiate w.r.t. x

$$22$$