# Class 12 Integration special type (Partial fraction)

5161

Mathematics Integration Level: Misc Level

Special type (Partial fraction)
When only even powers of x occur in the numerator as well as the denominator, substitute $x^{2}=y$ to make partial fractions. Once the partial fractions are formed substitute back $y=x^{2}$ and integrate.

$\int \frac{x^{2}}{x^{4}-x^{2}-12}dx=I$

5162

Mathematics Integration Level: Misc Level

Special type (Partial fraction)
When only even powers of x occur in the numerator as well as the denominator, substitute $x^{2}=y$ to make partial fractions. Once the partial fractions are formed substitute back $y=x^{2}$ and integrate.

$\int \frac{x^{2}}{1-x^{4}}dx$

5160

Mathematics Integration Level: Misc Level

Special type (Partial fraction)
When only even powers of x occur in the numerator as well as the denominator, substitute $x^{2}=y$ to make partial fractions. Once the partial fractions are formed substitute back $y=x^{2}$ and integrate.

$\int \frac{x^{2}}{(x^{2}+1)(x^{2}+4)}dx=I$

5163

Mathematics Integration Level: Misc Level

Special type (Partial fraction)
When only even powers of x occur in the numerator as well as the denominator, substitute $x^{2}=y$ to make partial fractions. Once the partial fractions are formed substitute back $y=x^{2}$ and integrate.

$\int \frac{Sinx}{Sin4x}dx$

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