Final Answer
$\frac{4}{3}\left(x+7\right)^{3}+\left(2x-5\right)^{3}-x^{3}-\frac{21}{2}x^2+6x+C_0$
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Step-by-step Solution
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1
Find the integral
$\int\left(4\left(x+7\right)^2+6\left(2x-5\right)^2-3\left(x^2+7x-2\right)\right)dx$
Learn how to solve definition of derivative problems step by step online.
$\int\left(4\left(x+7\right)^2+6\left(2x-5\right)^2-3\left(x^2+7x-2\right)\right)dx$
Learn how to solve definition of derivative problems step by step online. Find the integral of 4(x+7)^2+6(2x-5)^2-3(x^2+7x+-2). Find the integral. Solve the product -3\left(x^2+7x-2\right). Solve the product -3\left(7x-2\right). Expand the integral \int\left(4\left(x+7\right)^2+6\left(2x-5\right)^2-3x^2-21x+6\right)dx into 5 integrals using the sum rule for integrals, to then solve each integral separately.
Final Answer
$\frac{4}{3}\left(x+7\right)^{3}+\left(2x-5\right)^{3}-x^{3}-\frac{21}{2}x^2+6x+C_0$