Find the general indefinite integralsintegral of x(x3+2)2dxintegral of 3x2(x3+1)4dx

The given integral of xx3+22dx = ∫xx3+22dx = ∫xx32+2(x3).2+22dx = ∫x7+4x4+4xdx =…

Answered: Find the general indefinite integrals…

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter9: Polynomial And Rational Functions

Section9.2: Remainder And Factor Theorems

Problem 51PS

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Question

Find the general indefinite integrals

integral of x(x³+2)²dx

integral of 3x²(x³+1)⁴dx

Expert Solution

Step 1

The given integral of $x {(x^{3} + 2)}^{2} d x$

= $\int x {(x^{3} + 2)}^{2} d x = \int x ({(x^{3})}^{2} + 2 (x^{3}) . 2 + 2^{2}) d x$

= $\int (x^{7} + 4 x^{4} + 4 x) d x$

= $\frac{x^{8}}{8} + \frac{4 x^{5}}{5} + \frac{4 x^{2}}{2} + c$ use $(\int x^{n} d x = \frac{x^{n + 1}}{n + 1})$

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A polynomial of degree n I has exactly ____________________zero if a zero of multiplicity m is counted m times.

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Find the general indefinite integrals integral of x(x3+2)2dx integral of 3x2(x3+1)4dx