Indicate the u-substitution.(a) 3x2(1 + x3)25 dx =u25 du if u =and du = .(b) 2x sin x2

Chapter 5, Problem 1

(choose chapter or problem)

Indicate the u-substitution.

(a)  \(\int 3 x^{2}\left(1+x^{3}\right)^{25} d x=\int u^{25} d u\) if u = ________ and du = _________.

(b)  \(\int 2 x \sin x^{2} d x=\int \sin u d u\)  if u = __________ and du = __________.

(c) \(\int \frac{18 x}{1+9 x^{2}} d x=\int \frac{1}{u} d u\)  if u = ___________ and du = ____________.

(d) \(\int \frac{3}{1+9 x^{2}} d x=\int \frac{1}{1+u^{2}} d u\)  if u = ___________ and du = ____________.

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Text Transcription:

integral 3x^2 (1+x^3)^25 dx=integral u^25 du

integral 2x sin x^2 dx=integral sin u du

integral 18x/1+9x^2 dx=integral 1/u du

integral 3/1+9x^2 dx=integral 1/1+u^2 du