Evaluate the following integrals. Include absolute values only when needed. ∫0555xdx

Question

Evaluate the following integrals. Include absolute values only when needed.  ∫0555xdx

Piosellisf · Accepted Answer

Step 1  Consider the following integral:  ∫0555xdx  Substitute 5x=u⇒5dx=du⇒dx=15du in the above integral:  ∫0555xdx=∫055u5du  =[5u5×ln⁡(5)]05  =[5u−1ln⁡(5)]05  Step 2  Substitute u=5x:  ∫0555xdx=[55x−1ln⁡(5)]05  =525−15×ln⁡(5)  Step 3  Hence, the solution is 525−15×ln⁡(5).

Thomas White · Accepted Answer

∫55xdx  Substitution u=5x  =15∫5udu  Now we calculate:  ∫5udu  Integral of exponential function:  ∫audu=auln⁡(a) at: a=5  =5uln⁡(5)  We substitute the already calculated integrals:  15∫5udu  =5u−1ln⁡(5)  Reverse replacement u=5x:  =55x−1ln⁡(5)  Problem solved:  ∫55xdx  =55x−1ln⁡(5)+C

nick1337 · Accepted Answer

∫55xdx Transform the expression ∫5t×15dt Use properties of integrals 15×∫5tdt Evaluate the integral 15×5tln⁡(5) Substitute back 15×55xln⁡(5) Simplify 55x−1ln⁡(5) Add C Solution 55x−1ln⁡(5)+C

Evaluate the following integrals. Include absolute values only when needed. \int_{0}^{5}5^{5x}dx

Answered question

Answer & Explanation

New Questions in Calculus 2