Find indefinite integral. ∫−3e2xdx

Question

Find indefinite integral.  ∫−3e2xdx

twineg4 · Accepted Answer

Step 1  For an integral of the form ∫cf(x)dx where c is a constant the integral is equal to c∫f(x)dx. For the problem use the integral ∫exdx=ex+C.  To reduce the integral to this form use a substitution and then use the first property mentioned above. The constant C here is the constant of integration.  Step 2  The given integral is ∫−3e2xdx. This is equivalent to −3∫e2xdx. Use the substitution u=2x. This gives dx=du2. Substitute in the integral to calculate the indefinite integral.  ∫−3e2xdx=−3∫e2xdx  =−3∫eudu2  =−32∫eudu  =−1.5eu+C  =−1.5e2x+C

Paul Mitchell · Accepted Answer

∫−3e2xdx  Substitution u=2x⇒dudx=2⇒dx=12du:  =−32∫eudu  Now we calculate:  ∫eudu  Integral of exponential function:  ∫audu=auln⁡(a) at a=e:  =eu  We substitute the already calculated integrals:  −32∫eudu  =−3eu2  Reverse replacement u=2x:  =−3e2x2  Problem solved:  ∫−3e2xdx  =−3e2x2+C

nick1337 · Accepted Answer

∫(−3∗e2∗x)∗dx We represent the initial integral in the form: ∫(−3∗e2∗x)∗dx=∫−3∗e2∗x∗dx ∫(−3∗e2∗x)∗dx This is a tabular integral: ∫−3∗e2∗x∗dx=−3∗e2∗x2+C

Find indefinite integral. \int -3e^{2x}dx

Answered question

Answer & Explanation

New Questions in Calculus 2