Calculus Examples

$\int t (3 t^{3} + 1) d x$

Step 1

Multiply $t (3 t^{3} + 1)$ .

$\int t (3 t^{3}) + t \cdot 1 d x$

Step 2

Simplify.

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Step 2.1

Raise $t$ to the power of $1$ .

$\int 3 (t^{1} t^{3}) + t \cdot 1 d x$

Step 2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int 3 t^{1 + 3} + t \cdot 1 d x$

Step 2.3

Add $1$ and $3$ .

$\int 3 t^{4} + t \cdot 1 d x$

Step 2.4

Multiply $t$ by $1$ .

$\int 3 t^{4} + t d x$

Step 3

Split the single integral into multiple integrals.

$\int 3 t^{4} d x + \int t d x$

Step 4

Apply the constant rule.

$3 t^{4} x + C + \int t d x$

Step 5

Apply the constant rule.

$3 t^{4} x + C + t x + C$

Step 6

Simplify.

$3 t^{4} x + t x + C$