Calculus Examples

$\int 13.897 t + \frac{284.653}{t} d t$

Step 1

Split the single integral into multiple integrals.

$\int 13.897 t d t + \int \frac{284.653}{t} d t$

Step 2

Since $13.897$ is constant with respect to $t$ , move $13.897$ out of the integral.

$13.897 \int t d t + \int \frac{284.653}{t} d t$

Step 3

By the Power Rule, the integral of $t$ with respect to $t$ is $\frac{1}{2} t^{2}$ .

$13.897 (\frac{1}{2} t^{2} + C) + \int \frac{284.653}{t} d t$

Step 4

Since $284.653$ is constant with respect to $t$ , move $284.653$ out of the integral.

$13.897 (\frac{1}{2} t^{2} + C) + 284.653 \int \frac{1}{t} d t$

Step 5

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

$13.897 (\frac{1}{2} t^{2} + C) + 284.653 (\ln (| t |) + C)$

Step 6

Simplify.

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Step 6.1

Simplify.

$13.897 (\frac{1}{2}) t^{2} + 284.653 \ln (| t |) + C$

Step 6.2

Combine fractions.

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Step 6.2.1

Combine $13.897$ and $\frac{1}{2}$ .

$\frac{13.897}{2} t^{2} + 284.653 \ln (| t |) + C$

Step 6.2.2

Divide $13.897$ by $2$ .

$6.9485 t^{2} + 284.653 \ln (| t |) + C$