Calculus Examples

$\int_{1}^{2} {(t + \frac{1}{t})}^{2} d x$

Step 1

Apply the constant rule.

${(t + \frac{1}{t})}^{2} x]_{1}^{2}$

Step 2

Substitute and simplify.

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Step 2.1

Evaluate ${(t + \frac{1}{t})}^{2} x$ at $2$ and at $1$ .

$({(t + \frac{1}{t})}^{2} \cdot 2) - {(t + \frac{1}{t})}^{2} \cdot 1$

Step 2.2

Simplify.

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Step 2.2.1

Move $2$ to the left of ${(t + \frac{1}{t})}^{2}$ .

$2 \cdot {(t + \frac{1}{t})}^{2} - {(t + \frac{1}{t})}^{2} \cdot 1$

Step 2.2.2

Multiply $- 1$ by $1$ .

$2 {(t + \frac{1}{t})}^{2} - {(t + \frac{1}{t})}^{2}$

Step 2.2.3

Subtract ${(t + \frac{1}{t})}^{2}$ from $2 {(t + \frac{1}{t})}^{2}$ .

${(t + \frac{1}{t})}^{2}$

Step 3