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. \(\int\) (cotx) dx = log |sin x| + C or, \(\int\) […]
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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. \(\int\) (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. \(\int\) (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. \(\int\) (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 \(px^2+qx+r\over {(x-a)(x-b)(x-c)}\) \(A\over {x-a}\) + \(B\over {x-b}\) + \(C\over {x-c}\) 2 \(px^2+qx+r\over {{(x-a)}^2(x-b)}\) \(A\over {x-a}\) + \(B\over {(x-a)}^2\)
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Here you will learn integration of trigonometric function with examples. Let’s begin – Integration of Trigonometric Function (i) \(\int\) \(sin^mxcos^nx\) Case-1 : When both m & n \(\in\) 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) \(\int\) \({(ax+b)}^n\) dx = \({(ax+b)}^{n+1}\over {a(n+1)}\) + C ; n \(\ne\) -1 (ii) \(\int\) \(dx\over {ax+b}\) dx = \(1\over a\) ln|ax+b| + C (iii) \(\int\) \(e^{ax+b}\) dx = \({1\over {a}}e^{ax+b}\) + C or \(\int\) \(e^x\) =
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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 – \(\int\) u.v dx = u \(\int\) v dx – \(\int\)[\(du\over dx\).\(\int\)v dx]dx i.e The integral of the product of two functions = (first function) \(\times\) (Integral of Second function) – Integral of
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