Alyssa R.
asked • 01/12/22Integral Question
Would anyone be able to help me solve this integral?
∫ (5x)^5 √(5x)^3 + 1 dx
More
1 Expert Answer
Yefim S. answered • 01/12/22
Tutor
5
(20)
Math Tutor with Experience
∫ (5x)^5 √(5x)^3 + 1 dx. y = 5x
∫ (5x)^5 √(5x)^3 + 1 dx = 1/5∫y5(y3 + 1)1/2dy = y3 + 1 = z; 3y2dy = dz; dy = dz/(3y2); z = (5x)3 + 1
= 1/15∫y5z1/2dz/y2 = 1/15∫y3z1/2dz = 1/15∫(z - 1)z1/2dz = 1/15(z3/2 - z1/2)dz = 1/15(2/5z5/2 - 2/3z3/2) + C =
2/75[(5x)3 + 1]5/2 - 1/45[(5x)3 + 1]3/2 + C
Still looking for help? Get the right answer, fast.
Ask a question for free
Get a free answer to a quick problem.
Most questions answered within 4 hours.
OR
Find an Online Tutor Now
Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.
Doug C.
Is the +1 under the radical or outside?01/12/22