Find the following indefinite integral:∫(2𝑥6)d𝑥=
Question
Find the following indefinite integral:∫(2𝑥6)d𝑥=
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Solution
To find the indefinite integral of the function 2x^6 dx, you can use the power rule for integration, which states that the integral of x^n dx is (1/(n+1))x^(n+1) + C, where C is the constant of integration.
Step 1: Identify the power of x, which is 6 in this case.
Step 2: Add 1 to the power of x, which gives you 6 + 1 = 7.
Step 3: Divide the coefficient of x (which is 2) by the new power of x (which is 7). This gives you 2/7.
Step 4: Write down the new power of x, which is x^7.
Step 5: Don't forget to add the constant of integration, C.
So, the indefinite integral
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