Calculus Examples

$\int_{0}^{1} \frac{e^{5 x}}{e^{3 x}} d u$

Step 1

Cancel the common factor of $e^{5 x}$ and $e^{3 x}$ .

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Step 1.1

Factor $e^{3 x}$ out of $e^{5 x}$ .

$\int_{0}^{1} \frac{e^{3 x} e^{2 x}}{e^{3 x}} d u$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Multiply by $1$ .

$\int_{0}^{1} \frac{e^{3 x} e^{2 x}}{e^{3 x} \cdot 1} d u$

Step 1.2.2

Cancel the common factor.

$\int_{0}^{1} \frac{e^{3 x} e^{2 x}}{e^{3 x} \cdot 1} d u$

Step 1.2.3

Rewrite the expression.

$\int_{0}^{1} \frac{e^{2 x}}{1} d u$

Step 1.2.4

Divide $e^{2 x}$ by $1$ .

$\int_{0}^{1} e^{2 x} d u$

Step 2

Apply the constant rule.

$e^{2 x} u]_{0}^{1}$

Step 3

Substitute and simplify.

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Step 3.1

Evaluate $e^{2 x} u$ at $1$ and at $0$ .

$(e^{2 x} \cdot 1) - e^{2 x} \cdot 0$

Step 3.2

Simplify.

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Step 3.2.1

Multiply $e^{2 x}$ by $1$ .

$e^{2 x} - e^{2 x} \cdot 0$

Step 3.2.2

Multiply $0$ by $- 1$ .

$e^{2 x} + 0 e^{2 x}$

Step 3.2.3

Multiply $0$ by $e^{2 x}$ .

$e^{2 x} + 0$

Step 3.2.4

Add $e^{2 x}$ and $0$ .

$e^{2 x}$

Step 4