Mathematical Proofs

25
Feb
Pattern – 2 : Indefinite Integration

⋆ Pattern – 2 :

If ∫f(x) dx = F(x) +c, then

∫ f (a + b) dx = \frac{1}{a} F ( ax + b )dx + c  :  a ≠ 0

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Tags: math maths, formula, any, Definite, integration, math, pattern, of, dx, maths, 1/a, mathematics, sabiti, ganit, proof, f(ax+b), definition,
24
Feb
Pattern - 43(iv) of Indefinite Integration

⋆ Pattern – 43 (iv)

Integrals of differential binomials and chebyslev’s  criterion

\int x^m\left(a+bx^n\right)^p\ dx

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24
Feb
Pattern - 43(iii) of Indefinite Integration

⋆ Pattern –  43(iii) :

Integrals of differential binomials and chebyslev’s  criterion

\int x^m\left(a+bx^n\right)^p\ dx

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Tags: math, ganit, integration, pattern, indefinite, sabiti,
24
Feb
Pattern - 43(ii) of Indefinite Integration

⋆ Pattern – 43 (ii)

Integrals of differential binomials and chebyslev’s  criterion

∫dx  : p ≠ 0

(ii) If p is a negative integer and m,n are rational numbers, put x = t^k

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Tags: math, ganit, integration, pattern, indefinite, sabiti,
24
Feb
Pattern - 43(i) of Indefinite Integration

⋆ Pattern – 43(i)

Integrals of differential binomials and chebyslev’s  criterion

x^m\left(a+bx^n\right)^p\ dx  : p ≠ 0

(i) If …

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Posted in: Pattern - 43(i) of Indefinite Integration,
Tags: pattern, indefinite, sabiti, math, ganit, integration,
24
Feb
Pattern - 42 of Indefinite Integration

⋆ Pattern – 42

\int\frac{ax^2+bx+c}{\left(qx+4\right)\sqrt{px^2+1x+r}}\ dx

Substitute :

Nr = A(gx…

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Posted in: Pattern - 42 of Indefinite Integration,
Tags: math, ganit, integration, pattern, indefinite, sabiti,