Math  /  Calculus

QuestionSolve the following: show your complete solutions 1) (42x+2x2+3)dx\int\left(42 x+2 x^{2}+3\right) d x 2.) 2512x43dx\int^{2} \sqrt[3]{512 x^{4}} d x 3.) 5x343xdx\int \frac{5 x^{3}-4}{3 x} d x

Studdy Solution
Combine all the integrated terms and add the constant of integration CC. (5x2343x)dx=5x3943lnx+C \int \left( \frac{5x^2}{3} - \frac{4}{3x} \right) \, dx = \frac{5x^3}{9} - \frac{4}{3} \ln|x| + C
Solution:
1. (42x+2x2+3)dx=21x2+2x33+3x+C\int(42 x+2 x^{2}+3) d x = 21x^2 + \frac{2x^3}{3} + 3x + C
2. 2512x43dx=1927\int^{2} \sqrt[3]{512 x^{4}} d x = \frac{192}{7}
3. 5x343xdx=5x3943lnx+C\int \frac{5 x^{3}-4}{3 x} d x = \frac{5x^3}{9} - \frac{4}{3} \ln|x| + C

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