intgartion of x square add 4 …
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Posted by Anuj Sehrawat 7 years, 5 months ago
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Prabjeet Singh 7 years, 5 months ago
{tex}I=\int\cfrac {x^2+4}{x^2+16}dx{/tex}
{tex}\text {Since, the degree of numerator anmd denominator are same, so dividing we get}{/tex}
{tex}I= \int \bigg[ 1-\cfrac{12}{x^2+16} \bigg]dx {/tex}
{tex}\Rightarrow I=\int dx-12\int {\cfrac {1}{x^2+16}}dx{/tex}
{tex}\Rightarrow I = x-12\int \cfrac {1}{x^2+(4)^2} dx{/tex}
{tex}\Rightarrow I=x-12\Bigg[\cfrac {1}{4} \text { tan}^{-1} \cfrac {x}{4}\Bigg]+c{/tex}
{tex}\Rightarrow I=x-3 \text { tan}^{-1} \cfrac {x}{4} +c{/tex}
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