Formula for integration by parts: ∫ uvdx=u v dx ∫ u'( vdx)dx ∫uvdx=∫ u×(1v)dx Applying integration by parts formula ∴∫uvdx=u∫(1v)dx ∫ u'(1vdx)dx . ...

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Standard XII

Mathematics

Integration by Parts

Solve : ∫uv...

Question

Solve :
$\int \frac{u}{v} d x$

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Solution

Formula for integration by parts:
$\int u v d x = u v d x - \int u^{'} (v d x) d x$
$\int \frac{u}{v} d x = \int u \times (\frac{1}{v}) d x$
Applying integration by parts formula
$∴ \int \frac{u}{v} d x = u \int (\frac{1}{v}) d x - \int u^{'} (\frac{1}{v} d x) d x$ .

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Solve : ∫uvdx

Formula for integration by parts:∫uvdx=uvdx−∫u′(vdx)dx∫uvdx=∫u×(1v)dxApplying integration by parts formula∴∫uvdx=u∫(1v)dx−∫u′(1vdx)dx.

Solve :
$\int \frac{u}{v} d x$

Formula for integration by parts:
$\int u v d x = u v d x - \int u^{'} (v d x) d x$
$\int \frac{u}{v} d x = \int u \times (\frac{1}{v}) d x$
Applying integration by parts formula
$∴ \int \frac{u}{v} d x = u \int (\frac{1}{v}) d x - \int u^{'} (\frac{1}{v} d x) d x$ .