Mathematics

Evaluate the following integration w.r.t. $$x$$
 $$\int \dfrac {1}{(4x+5)^{2}+1}dx$$


SOLUTION
According to question,

$$\int \dfrac{1}{(4x+5)^2+1}dx$$

Let $$4x+5=t$$

$$\implies 4dx=dt$$

Hence,
$$\dfrac{1}{4}\int \dfrac{1}{(t)^2+1}dx$$

$$\implies \dfrac{1}{4}tan^{-1}t+C$$

$$\implies \dfrac{1}{4}tan^{-1}(4x+5)+C$$
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Subjective Medium Published on 17th 09, 2020
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