Exercise
$\int\left(4e^x-a^{-x}\right)dx$
Step-by-step Solution
Learn how to solve integrals of exponential functions problems step by step online. Find the integral int(4e^x-a^(-x))dx. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. Expand the integral \int\left(4e^x+\frac{-1}{a^x}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int4e^xdx results in: 4e^x. The integral \int\frac{-1}{a^x}dx results in: \frac{1}{a^x\ln\left(a\right)}.
Find the integral int(4e^x-a^(-x))dx
Final answer to the exercise
$4e^x+\frac{1}{a^x\ln\left|a\right|}+C_0$