Find intleft(4 x^{5}+2 x^{6}right) d x

Question

Accepted Answer

Step:1 ：Split the integral into two parts: (int 4x^5 dx) and (int 2x^6 dx).Step:2 ：Find the integral of each part separately using the rule (int x^n dx = frac{1}{n+1}x^{n+1}).Step:3 ：For the first part, (int 4x^5 dx = 4 int x^5 dx = 4 cdot frac{1}{5+1}x^{5+1} = frac{4}{6}x^6).Step:4 ：For the second part, (int 2x^6 dx = 2 int x^6 dx = 2 cdot frac{1}{6+1}x^{6+1} = frac{2}{7}x^7).Step:5 ：Add the results of the two integrals together to get the final answer: (frac{2}{7}x^7 + frac{2}{3}x^6 + C), where (C) is the constant of integration.Step:6 ：(boxed{frac{2}{7}x^7 + frac{2}{3}x^6 + C}) is the final answer.

Answer

Step: 1 ：Split the integral into two parts: (int 4x^5 dx) and (int 2x^6 dx).Step: 2 ：Find the integral of each part separately using the rule (int x^n dx = frac{1}{n+1}x^{n+1}).Step: 3 ：For the first part, (int 4x^5 dx = 4 int x^5 dx = 4 cdot frac{1}{5+1}x^{5+1} = frac{4}{6}x^6).Step: 4 ：For the second part, (int 2x^6 dx = 2 int x^6 dx = 2 cdot frac{1}{6+1}x^{6+1} = frac{2}{7}x^7).Step: 5 ：Add the results of the two integrals together to get the final answer: (frac{2}{7}x^7 + frac{2}{3}x^6 + C), where (C) is the constant of integration.Step: 6 ：(boxed{frac{2}{7}x^7 + frac{2}{3}x^6 + C}) is the final answer.

Find $\int (4 x^{5} + 2 x^{6}) d x$

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Find ∫(4x5+2x6)dx

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Find $\int (4 x^{5} + 2 x^{6}) d x$