Evaluate the Integrals 1) ∫(t^(1/7))(sin(t^(8/7)-3)dt?
Evaluate the Integrals:
1) ∫(t^(1/7))(sin(t^(8/7)-3)dt
2) ∫(cos(6x+4))/(sin^2(6x+4))dx
Please explain to me how to do these problems step by step. Thank You :)
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u = t^(8/7) - 3
du = (8/7) * t^(1/7) * dt
t^(1/7) * sin(t^(8/7) - 3) * dt =>
(7/8) * sin(u) * du
Integrate
(-7/8) * cos(u) + C =>
(-7/8) * cos(t^(8/7) - 3) + C
cos(6x + 4) * dx / sin(6x + 4)^2
u = sin(6x + 4)
du = 6 * cos(6x + 4) * dx
(1/6) * du / u^2
Integrate
(-1/6) / u + C =>
-1/(6 * u) + C =>
-1/(6 * sin(6x + 4)) + C