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Exercise

$\int x^3\cos^2\left(3x\right)dx$

Step-by-step Solution

1

The integral of a constant is equal to the constant times the integral's variable

$x^3x\cos\left(3x\right)^2$
2

When multiplying exponents with same base you can add the exponents: $x^3x\cos\left(3x\right)^2$

$x^{4}\cos\left(3x\right)^2$
3

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

$x^{4}\cos\left(3x\right)^2+C_0$

Final answer to the exercise

$x^{4}\cos\left(3x\right)^2+C_0$

Try other ways to solve this exercise

  • Choose an option
  • 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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Main Topic: Integrals of Polynomial Functions

Integrals of polynomial functions.

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