Question

Integrate the following functions with respect to x
(v)
4x+1/
✓ 2x²+x-3​

Answer 1

★ Solution :

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$\int \frac{4x + 1}{ \sqrt{2 {x}^{2} + x - 3 } } dx\\ \\ \\ let, \: 2 {x}^{2} + x = t \\ \\ \implies \: (4x + 1)dx = dt \\ \\ \\ substituting, \\ \\ \int \frac{1}{ \sqrt{t - 3 } } dt \\ \\ \implies\ln |t - 3| + c \: \: \\ \\ \: \: \: \: \: \big[ \tt \: c \: \: is \: integral \: constant \big]\\ \\ \implies \bf \ln |2 {x}^{2} + x - 3 | + c$

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