Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Find the integral
- Exact Differential Equation
- Linear Differential Equation
- Separable Differential Equation
- Homogeneous Differential Equation
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
- Integrate by parts
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Find the integral
Learn how to solve integral calculus problems step by step online.
$\int\ln\left(x^3\sqrt{x+9}\right)dx$
Learn how to solve integral calculus problems step by step online. Find the integral of y=ln(x^3(x+9)^1/2). Find the integral. Apply properties of logarithms to expand and simplify the logarithmic expression \ln\left(x^3\sqrt{x+9}\right) inside the integral. Expand the integral \int\left(3\ln\left(x\right)+\frac{1}{2}\ln\left(x+9\right)\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. Multiply the single term 3 by each term of the polynomial \left(x\ln\left(x\right)-x\right).