Calculus Examples

$\int 4 + 5 t^{\frac{2}{3}} d t$

Step 1

Split the single integral into multiple integrals.

$\int 4 d t + \int 5 t^{\frac{2}{3}} d t$

Step 2

Apply the constant rule.

$4 t + C + \int 5 t^{\frac{2}{3}} d t$

Step 3

Since $5$ is constant with respect to $t$ , move $5$ out of the integral.

$4 t + C + 5 \int t^{\frac{2}{3}} d t$

Step 4

By the Power Rule, the integral of $t^{\frac{2}{3}}$ with respect to $t$ is $\frac{3}{5} t^{\frac{5}{3}}$ .

$4 t + C + 5 (\frac{3}{5} t^{\frac{5}{3}} + C)$

Step 5

Simplify.

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Step 5.1

Simplify.

$4 t + 5 (\frac{3}{5}) t^{\frac{5}{3}} + C$

Step 5.2

Simplify.

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Step 5.2.1

Combine $5$ and $\frac{3}{5}$ .

$4 t + \frac{5 \cdot 3}{5} t^{\frac{5}{3}} + C$

Step 5.2.2

Multiply $5$ by $3$ .

$4 t + \frac{15}{5} t^{\frac{5}{3}} + C$

Step 5.2.3

Cancel the common factor of $15$ and $5$ .

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Step 5.2.3.1

Factor $5$ out of $15$ .

$4 t + \frac{5 \cdot 3}{5} t^{\frac{5}{3}} + C$

Step 5.2.3.2

Cancel the common factors.

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Step 5.2.3.2.1

Factor $5$ out of $5$ .

$4 t + \frac{5 \cdot 3}{5 (1)} t^{\frac{5}{3}} + C$

Step 5.2.3.2.2

Cancel the common factor.

$4 t + \frac{5 \cdot 3}{5 \cdot 1} t^{\frac{5}{3}} + C$

Step 5.2.3.2.3

Rewrite the expression.

$4 t + \frac{3}{1} t^{\frac{5}{3}} + C$

Step 5.2.3.2.4

Divide $3$ by $1$ .

$4 t + 3 t^{\frac{5}{3}} + C$