Consider the indefinite integral ? (x + 4) / (4x + 3)² dx. The substitution u = 4x + 3 transforms the integral into which of the following? A. ? (u + 13) / (16u²) du B. ? (u + 4) / (4u²) du C. ? (4u + 7) / (u²) du D. ? (u + 13) / (u²) du E. ? (u + 13) / (4u²) du F. ? (u + 4) / (4u + 3)² du G. ? (u + 4) / (u²) du H. ? (4u + 7) / (4u²) du
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We can differentiate both sides with respect to $x$ to find $du$: $$\frac{du}{dx} = 4$$ Now, we can solve for $dx$: $$dx = \frac{1}{4} \, du$$ Show more…
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