Mathematics

Solve $$I=\int \frac{4x+1}{\sqrt{2x^{2}+x-3}}$$


SOLUTION
$$I=\int{\dfrac{4x+1}{\sqrt{2{x}^{2}+x-3}}}dx$$
Let $$2x^{2}+x-3=t$$
Differentiating, $$\left(4x+1\right)dx=dt$$
$$\therefore I=\int{\dfrac{dt}{\sqrt{t}}}$$
$$=2t^{1/2}$$
$$=2 (2{x^{2}+x-3})^{1/2}$$

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Subjective Medium Published on 17th 09, 2020
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