Mathematical Proofs

24
Feb
Pattern - 39 of Indefinite Integration

Pattern – 39 :

\int\frac{ax+b}{\left(px^2+qx+r\right)\ \sqrt{mx+n\ }}dx\ \ \ or\ \ \

\int\frac{1}{\left(px^2+qx+r\right)\ \sqrt{mx+n}}dx,\ then\ put\ mx+n=t^2

 

1) Evaluate :

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24
Feb
Pattern - 37 of Indefinite Integration

⋆ Pattern – 37

\int\frac{1}{\sqrt{\left(x-a\right)\left(b-x\right)}}dx,\ \int\sqrt{\fr...
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20
Feb
Pattern - 36 of Indefinite Integration

Pattern 36 :

\ I_n=\ \int\left(\log{x}\right)^n\ dx, then

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20
Feb
Pattern - 35 of Indefinite Integration

⋆ Pattern – 35

I_n=\ \int x^n\ e^{ax}\ dx

∴ 

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20
Feb
Pattern - 34 of Indefinite Integration

⋆ Pattern – 34

I_n=\ \int x^n sin mx dx, then I_...
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20
Feb
Pattern - 33 of Indefinite Integration

⋆ Pattern – 33

I_n=\ \int x^n sin\ mx\ dx, then I_n

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20
Feb
Pattern - 32 of Indefinite Integration

⋆ Pattern – 32

I_n=\cos^n{x} dx

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