समाकलन के सूत्र (Integration Formulas)

समाकलन के सूत्र (Integration Formulas) PDF Download

Here Are Some Important Formulas Of Integration. These Formulas Are Very Important For Those Students Who Are Related To Mathematics or physics.So here we provide The PDF File of these very important formulas of Integration .

➢ ∫x ⁿ ∙dx =

x ^{n + 1} / n + 1

+ C

➢ ∫e ^x ∙dx = e ^x + C

➢ ∫e ^{- x} ∙dx = - e ^{- x} + C

➢ ∫

1 / x

∙dx = logx+ C

➢ ∫Sinx∙dx = - Cosx + C

➢ ∫Cosx∙dx = Sinx + C

➢ ∫Tanx∙dx = log Secx + C

➢ ∫Cotx∙dx = log Sinx + C

➢ ∫Secx∙dx = log |Secx + Tanx | + C

➢ ∫Cosecx∙dx = log |Cosecx - Cotx | + C

➢ ∫

1 / √1 - x ²

∙dx = Sin ^-1x + C

➢ ∫

1 / 1 + x ²

∙dx = Tan ^-1x + C

➢ ∫

1 / x√x ² - 1

∙dx = Sec ^-1x + C

➢ ∫

1 / √a ² - x ²

∙dx = Sin ^-1(

x / a

) + C

➢ ∫

1 / √x ² - a ²

∙dx = log | x + √x ² - a ² | + C

➢ ∫

1 / √x ² + a ²

∙dx = log | x + √x ² + a ² | + C

➢ ∫√ a ² - x ² ∙dx =

x / 2

√ a ² - x ² +

a ² / 2

Sin ^-1(

x / a

) + C

➢ ∫√ a ² + x ² ∙dx =

x / 2

√ a ² + x ² +

a ² / 2

log | x + √ x ² + a ² | + C

➢ ∫√ x ² - a ² ∙dx =

x / 2

√ x ² - a ² -

a ² / 2

log | x + √ x ² - a ² | + C

➢ ∫

1 / a ² - x ²

∙dx =

1 / 2a

log |

a + x / a - x

| + C

➢ ∫

1 / x ² - a ²

∙dx =

1 / 2a

log |

x - a / x + a

| + C

➢ ∫Sec ²x ∙dx = Tanx + C

➢ ∫Cosec ²x ∙dx = - Cotx + C

➢ ∫Secx ∙ Tanx ∙dx = Secx + C

➢ ∫Cosecx ∙ Cotx ∙dx = - Cosecx + C

➢ ∫K ∙dx = Kx + C (जहाँ K = अचर राशि )

➢ ∫

1 / x ² + a ²

∙dx =

1 / a

Tan^-1

x / a

+ C

Also Read-अवकलन के सूत्र ( Formulas of Differentiation )

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