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f(x)=5x(3x-2)^2−6−5−4−3−2−10123456−3-2.5−2-1.5−1-0.500.511.522.53xy

Exercise

∫5x(3x−2)2dx\int5x\left(3x-2\right)^2dx

Step-by-step Solution

Learn how to solve special products problems step by step online. Find the integral int(5x(3x-2)^2)dx. Rewrite the integrand 5x\left(3x-2\right)^2 in expanded form. Expand the integral \int\left(45x^{3}-60x^2+20x\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int45x^{3}dx results in: \frac{45}{4}x^{4}. The integral \int-60x^2dx results in: -20x^{3}.
Find the integral int(5x(3x-2)^2)dx

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Final answer to the exercise

454x4−20x3+10x2+C0\frac{45}{4}x^{4}-20x^{3}+10x^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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Main Topic: Special Products

Special products is the multiplication of algebraic expressions that follow certain rules and patterns, so you can predict the result without necessarily doing the multiplication.

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