Calculus Examples

$\int 7 x^{3} - 15 x + 10 d x$

Step 1

This integral could not be completed using u-substitution. Mathway will use another method.

Step 2

Split the single integral into multiple integrals.

$\int 7 x^{3} d x + \int - 15 x d x + \int 10 d x$

Step 3

Since $7$ is constant with respect to $x$ , move $7$ out of the integral.

$7 \int x^{3} d x + \int - 15 x d x + \int 10 d x$

Step 4

By the Power Rule, the integral of $x^{3}$ with respect to $x$ is $\frac{1}{4} x^{4}$ .

$7 (\frac{1}{4} x^{4} + C) + \int - 15 x d x + \int 10 d x$

Step 5

Since $- 15$ is constant with respect to $x$ , move $- 15$ out of the integral.

$7 (\frac{1}{4} x^{4} + C) - 15 \int x d x + \int 10 d x$

Step 6

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

$7 (\frac{1}{4} x^{4} + C) - 15 (\frac{1}{2} x^{2} + C) + \int 10 d x$

Step 7

Apply the constant rule.

$7 (\frac{1}{4} x^{4} + C) - 15 (\frac{1}{2} x^{2} + C) + 10 x + C$

Step 8

Simplify.

Tap for more steps...

Step 8.1

Simplify.

Tap for more steps...

Step 8.1.1

Combine $\frac{1}{4}$ and $x^{4}$ .

$7 (\frac{x^{4}}{4} + C) - 15 (\frac{1}{2} x^{2} + C) + 10 x + C$

Step 8.1.2

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

$7 (\frac{x^{4}}{4} + C) - 15 (\frac{x^{2}}{2} + C) + 10 x + C$

Step 8.2

Simplify.

$\frac{7 x^{4}}{4} - \frac{15 x^{2}}{2} + 10 x + C$

Step 9

Reorder terms.

$\frac{7}{4} x^{4} - \frac{15}{2} x^{2} + 10 x + C$