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Exercise

$\left(3x+5\right)\left(2x+3\right)$

Step-by-step Solution

1

Find the integral

$\int\left(3x+5\right)\left(2x+3\right)dx$
2

Rewrite the integrand $\left(3x+5\right)\left(2x+3\right)$ in expanded form

$\int\left(6x^2+19x+15\right)dx$
3

Expand the integral $\int\left(6x^2+19x+15\right)dx$ into $3$ integrals using the sum rule for integrals, to then solve each integral separately

$\int6x^2dx+\int19xdx+\int15dx$
4

The integral $\int6x^2dx$ results in: $2x^{3}$

$2x^{3}$
5

The integral $\int19xdx$ results in: $\frac{19}{2}x^2$

$\frac{19}{2}x^2$
6

The integral $\int15dx$ results in: $15x$

$15x$
7

Gather the results of all integrals

$2x^{3}+\frac{19}{2}x^2+15x$
8

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

$2x^{3}+\frac{19}{2}x^2+15x+C_0$

Final answer to the exercise

$2x^{3}+\frac{19}{2}x^2+15x+C_0$

Try other ways to solve this exercise

  • Find the integral
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Prove from LHS (left-hand side)
  • Load more...
Can't find a method? Tell us so we can add it.

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