MYTUTOR SUBJECT ANSWERS

926 views

∫(1 + 3√x + 5x)dx

For each term the aim is to raise the power of x by 1 and divide by the new power. 

For this question, each part of the expression can be looked at seperately to make things a bit easier:

∫(1 + 3√x + 5x)dx = ∫1dx + ∫3√xdx + ∫5xdx

The first part of the expression can be looked at as 1*x0, so the integral of this is 1*x = x

The second part is a bit more difficult as the power of x isnt a whole number so it can be written as 3*x1/2, the integral of this being     3*x3/2*(2/3) = 2x3/2, (the 2/3 comes from dividing by the new power).

Finally the integral of 5x is easier as the power of x is a whole number and so is easily calculated as 5/2*x2.

Then finally recombining the three part the final answer is:

∫(1 + 3√x + 5x)dx = x + 2x3/2 + (5/2)x+ c

(c is constant and can take any value, this isnt a majorly important part of the question)

Mary T. A Level Maths tutor, GCSE Maths tutor

2 years ago

Answered by Mary, an A Level Maths tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

350 SUBJECT SPECIALISTS

£26 /hr

Scott R.

Degree: PGCE Secondary Mathematics (Other) - Leeds University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“I am currently completing 2 PGCEs in Leeds. I have always had a passion for maths and my objective is to help as many as possible reach their full potential.”

£26 /hr

Samuel C.

Degree: Physics (Bachelors) - Durham University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Further Mathematics
Chemistry

“Hi, I'm Sam Crawford. I'm studying Maths and Physics at Durham University, with an offer from Cambridge for next year, and I absolutely love both subjects.”

£26 /hr

Edoardo M.

Degree: Mathematics (Bachelors) - Bath University

Subjects offered:Maths, .STEP.

Maths
.STEP.

“Hi! My name is Edoardo, and I'm a Maths student at the University of Bath. I would be really excited to start working with you. ”

About the author

Mary T.

Currently unavailable: for new students

Degree: Mathematics (Masters) - Durham University

Subjects offered:Maths

Maths

“About me: I am currently studying maths in my first year at Durham University. Not only do I have a love for my subject but also for teaching it. In my last year of sixth form I set up a school wide tutoring system which helped many ...”

You may also like...

Other A Level Maths questions

How do you find the gradient of a parametric equation at a certain point?

How do I integrate ln(x), using integration by parts?

Find the exact value of sin(75°). Give your answer in its simplest form.

How do you resolve forces?

View A Level Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok