Here you will learn proof of integration of cotx or cot x and examples based on it. Let’s begin – Integration of Cotx or Cot x The integration of cotx is log |sin x| + C or – log |cosec x| + C i.e. ∫ (cotx) dx = log |sin x| + C or, ∫ […]
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Here you will learn proof of integration of tanx or tan x and examples based on it. Let’s begin – Integration of Tanx or Tan x The integration of tanx is – log |cos x| + C or log |sec x| + C i.e. ∫ (tanx) dx = – log |cos x| + C or,
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Here you will learn proof of integration of cosx or cos x and examples based on it. Let’s begin – Integration of Cosx or Cos x The integration of cosx is sinx + C where C is the integration constant. i.e. ∫ (cosx) dx = sin x + C Proof : We will prove this
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Here you will learn proof of integration of sinx or sin x and examples based on it. Let’s begin – Integration of Sinx or Sin x The integration of sinx is -cosx + C where C is the integration constant. i.e. ∫ (sinx) dx = -cos x + C Proof : We will prove this
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Here you will learn integration by partial fraction formula and integration of irrational functions. Let’s begin – Integration by Partial Fraction Formula (i) Integration of Rational Functions S.No form of rational function form of partial fraction 1 px2+qx+r(x−a)(x−b)(x−c) Ax−a + Bx−b + Cx−c 2 px2+qx+r(x−a)2(x−b) Ax−a + B(x−a)2
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Here you will learn integration of trigonometric function with examples. Let’s begin – Integration of Trigonometric Function (i) ∫ sinmxcosnx Case-1 : When both m & n ∈ natural numbers. (a) If one of them is odd, then substitute for the term of even power. (b) If both are odd, substitute either of them. (c)
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Here you will learn Integration integration formulas for class 12. Let’s begin – Integration Formula for Class 12 (i) ∫ (ax+b)n dx = (ax+b)n+1a(n+1) + C ; n ≠ -1 (ii) ∫ dxax+b dx = 1a ln|ax+b| + C (iii) ∫ eax+b dx = 1aeax+b + C or ∫ ex =
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Formula for Integration by Parts If u and v are two functions of x, then the formula for integration by parts is – ∫ u.v dx = u ∫ v dx – ∫[dudx.∫v dx]dx i.e The integral of the product of two functions = (first function) × (Integral of Second function) – Integral of
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