Calculus Examples

$\int b^{2} - 5 b + 5 d b$

Step 1

Split the single integral into multiple integrals.

$\int b^{2} d b + \int - 5 b d b + \int 5 d b$

Step 2

By the Power Rule, the integral of $b^{2}$ with respect to $b$ is $\frac{1}{3} b^{3}$ .

$\frac{1}{3} b^{3} + C + \int - 5 b d b + \int 5 d b$

Step 3

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

$\frac{1}{3} b^{3} + C - 5 \int b d b + \int 5 d b$

Step 4

By the Power Rule, the integral of $b$ with respect to $b$ is $\frac{1}{2} b^{2}$ .

$\frac{1}{3} b^{3} + C - 5 (\frac{1}{2} b^{2} + C) + \int 5 d b$

Step 5

Apply the constant rule.

$\frac{1}{3} b^{3} + C - 5 (\frac{1}{2} b^{2} + C) + 5 b + C$

Step 6

Simplify.

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Step 6.1

Combine $\frac{1}{2}$ and $b^{2}$ .

$\frac{1}{3} b^{3} + C - 5 (\frac{b^{2}}{2} + C) + 5 b + C$

Step 6.2

Simplify.

$\frac{b^{3}}{3} - \frac{5 b^{2}}{2} + 5 b + C$

Step 7

Reorder terms.

$\frac{1}{3} b^{3} - \frac{5}{2} b^{2} + 5 b + C$