Calculus Examples

$\frac{d R}{d t} = 3.17 - \frac{6.671}{t}$

Step 1

Rewrite the equation.

$d R = (3.17 - \frac{6.671}{t}) d t$

Step 2

Integrate both sides.

Tap for more steps...

Step 2.1

Set up an integral on each side.

$\int d R = \int 3.17 - \frac{6.671}{t} d t$

Step 2.2

Apply the constant rule.

$R + C_{1} = \int 3.17 - \frac{6.671}{t} d t$

Step 2.3

Integrate the right side.

Tap for more steps...

Step 2.3.1

Split the single integral into multiple integrals.

$R + C_{1} = \int 3.17 d t + \int - \frac{6.671}{t} d t$

Step 2.3.2

Apply the constant rule.

$R + C_{1} = 3.17 t + C_{2} + \int - \frac{6.671}{t} d t$

Step 2.3.3

Since $- 1$ is constant with respect to $t$ , move $- 1$ out of the integral.

$R + C_{1} = 3.17 t + C_{2} - \int \frac{6.671}{t} d t$

Step 2.3.4

Since $6.671$ is constant with respect to $t$ , move $6.671$ out of the integral.

$R + C_{1} = 3.17 t + C_{2} - (6.671 \int \frac{1}{t} d t)$

Step 2.3.5

Multiply $6.671$ by $- 1$ .

$R + C_{1} = 3.17 t + C_{2} - 6.671 \int \frac{1}{t} d t$

Step 2.3.6

The integral of $\frac{1}{t}$ with respect to $t$ is $\ln (| t |)$ .

$R + C_{1} = 3.17 t + C_{2} - 6.671 (\ln (| t |) + C_{3})$

Step 2.3.7

Simplify.

$R + C_{1} = 3.17 t - 6.671 \ln (| t |) + C_{4}$

Step 2.4

Group the constant of integration on the right side as $C$ .

$R = 3.17 t - 6.671 \ln (| t |) + C$