Calculus Examples

$\int \frac{t + 1}{t} d t$

Step 1

Split the fraction into multiple fractions.

$\int \frac{t}{t} + \frac{1}{t} d t$

Step 2

Split the single integral into multiple integrals.

$\int \frac{t}{t} d t + \int \frac{1}{t} d t$

Step 3

Cancel the common factor of $t$ .

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Step 3.1

Cancel the common factor.

$\int \frac{t}{t} d t + \int \frac{1}{t} d t$

Step 3.2

Rewrite the expression.

$\int d t + \int \frac{1}{t} d t$

Step 4

Apply the constant rule.

$t + C + \int \frac{1}{t} d t$

Step 5

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

$t + C + \ln (| t |) + C$

Step 6

Simplify.

$t + \ln (| t |) + C$