Question
Evaluate the integrals using the indicated substitutions.(a) $\int 2 x\left(x^{2}+1\right)^{23} d x ; u=x^{2}+1$(b) $\int \cos ^{3} x \sin x d x ; u=\cos x$
Step 1
Step 1: For part (a), we are given the integral \(\int 2x(x^2 + 1)^{23} \, dx\) and the substitution \(u = x^2 + 1\). Show more…
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INTEGRATION
Integration by Substitution
evaluate
Evaluate the integrals by making the indicated substitutions. (a) $\int 2 x\left(x^{2}+1\right)^{23} d x ; u=x^{2}+1$ (b) $\int \cos ^{3} x \sin x d x ; u=\cos x$ (c) $\int \frac{1}{\sqrt{x}} \sin \sqrt{x} d x ; u=\sqrt{x}$ (d) $\int \frac{3 x d x}{\sqrt{4 x^{2}+5}} ; u=4 x^{2}+5$ (e) $\int \frac{x^{2}}{x^{3}-4} d x ; u=x^{3}-4$
Integration
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