Final Answer
$\frac{x^{4}}{4}+\frac{x^{3}b}{3}+\frac{x^{3}a}{3}+\frac{1}{2}bax^2+C_0$
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Step-by-step Solution
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1
Rewrite the integrand $x\left(x+a\right)\left(x+b\right)$ in expanded form
$\int\left(x^{3}+bx^2+x^2a+bax\right)dx$
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$\int\left(x^{3}+bx^2+x^2a+bax\right)dx$
Learn how to solve integral calculus problems step by step online. Find the integral int(x(x+a)(x+b))dx. Rewrite the integrand x\left(x+a\right)\left(x+b\right) in expanded form. Expand the integral \int\left(x^{3}+bx^2+x^2a+bax\right)dx into 4 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int x^{3}dx results in: \frac{x^{4}}{4}. The integral \int bx^2dx results in: \frac{x^{3}b}{3}.
Final Answer
$\frac{x^{4}}{4}+\frac{x^{3}b}{3}+\frac{x^{3}a}{3}+\frac{1}{2}bax^2+C_0$