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Exercise

$\int\left(\frac{\left(\frac{x^3}{3}\right)}{5x^2}\right)dx$

Step-by-step Solution

1

Simplify the expression

$\int\frac{x}{15}dx$
2

Take the constant $\frac{1}{15}$ out of the integral

$\frac{1}{15}\int xdx$
3

Applying the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a number or constant function, in this case $n=1$

$\frac{1}{15}\cdot \frac{1}{2}x^2$
4

Multiplying fractions $\frac{1}{15} \times \frac{1}{2}$

$\frac{1}{30}x^2$
5

As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$

$\frac{1}{30}x^2+C_0$

Final answer to the exercise

$\frac{1}{30}x^2+C_0$

Try other ways to solve this exercise

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  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Integrate using trigonometric identities
  • Integrate using basic integrals
  • Product of Binomials with Common Term
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Similar Questions Solved

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$\int\left(dx\div x^2\sqrt{9-x^2}\right)$

$\int\frac{x^2dx}{\left(9-x^2\right)^{\frac{3}{2}}}$

$\int\frac{dx}{x\sqrt{x^{2}+36}}$

$\int\frac{\left(x^2-16\right)^{\frac{3}{2}}}{x^3}dx$

Main Topic: Integrals of Rational Functions

Integrals of rational functions of the form R(x) = P(x)/Q(x).

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