WebDec 12, 2016 · − 1 x +c Explanation: For this antiderivative, you would use the power rule for antiderivatives/integrals. This states that ∫xn = 1 n + 1 (xn+1). Since 1 x2 = x−2 and n ≠ − 1 in this case, you can apply this power rule. Answer: ∫ … WebThis gets important when you start learning standard integral forms. For example, here is a standard integral form: ∫ cos (u) du = sin (u) + C So, some students will incorrectly see: ∫ cos (x²) dx and say its integral must be sin (x²) + C. But this is wrong. Since you are treating x² as the u, you must have the derivative of x² as your du.

Introduction to Integration - Math is Fun

WebIntegrate by parts, where u = 1 / x, and v ′ = ex. Then u ′ = − 1 / x2, and v = ex. So, ∫ex x dx = ex x + ∫ex x2 dx Integrate by parts again, u = 1 / x2, v ′ = ex, so that u ′ = − 2 / x3 and v = ex. So, ∫ex x dx = ex x + ex x2 + 2∫ex x3 dx Repeat this process ad infinitum to get, ∫ex x dx = ex x + ex x2 + 2(ex x3 + 3(ex x4 + 4(ex x5 + ⋯))) WebIt is written as: ∫ sin (x) dx = −cos (x) + C Example: what is the integral of 1/x ? From the table above it is listed as being ln x + C It is written as: ∫ (1/x) dx = ln x + C The vertical bars either side of x mean absolute value, … img boys basketball coach

Integration Rules - Math is Fun

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