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$\int\left(a^{\left(x+1\right)}-2b^{\left(x-1\right)}\right)\left(2b^{\left(x-1\right)}+a^{\left(x+1\right)}\right)dx$
Learn how to solve problems step by step online. Integrate the function (a^(x+1)-2b^(x-1))(2b^(x-1)+a^(x+1)). Find the integral. Rewrite the integrand \left(a^{\left(x+1\right)}-2b^{\left(x-1\right)}\right)\left(2b^{\left(x-1\right)}+a^{\left(x+1\right)}\right) in expanded form. Expand the integral \int\left(a^{\left(2x+2\right)}-4b^{\left(2x-2\right)}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int a^{\left(2x+2\right)}dx results in: \frac{a^{\left(2x+2\right)}}{2\ln\left(a\right)}.