Find the general indefinite integrals, integral of x^2 square root of (x^3+1)dx, integral of pi sin x cos^3x dx

boske9s

boske9s

Open question

2022-08-19

Find the general indefinite integrals
integral of x2 square root of (x3+1)dx
integral of πsinxcos3xdx

Answer & Explanation

Carmelo Peck

Carmelo Peck

Beginner2022-08-20Added 12 answers

Step 1
Given: I=x2x3+1 dx 
for evaluating given integral, in given integral we substitute
x3+1=t...(1)
now, differentiating equation (1) with respect to x
d dx (x3+1)= dt  dx    (d dx (xn)=nxn1)
3x2+0= dt  dx 
3x2= dt  dx 
x2 dx = dt 3
Step 2
now, replace (x3+1) with t, x2 dx  with  dt 3 in given integral
so,
x2x3+1 dx =13t dt 
=13(t12+112+1)+c
=13(t32(32))+c
=2t329+c
=2(x3+1)329+c
hence, given integral is equal to 2(x3+1)329+c.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?