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Apply the formula: $\int a^ndx$$=\int newton\left(a^n\right)dx$, where $a^n=\left(3x^2+1\right)^6$, $a=3x^2+1$, $inta^n=\int\left(3x^2+1\right)^6$, $inta^n$dx=\int\left(3x^2+1\right)^6dx$ and $n=6$
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$\int\left(729x^{12}+1458x^{10}+1215x^{8}+540x^{6}+135x^{4}+18x^2+1\right)dx$
Learn how to solve problems step by step online. Find the integral int((3x^2+1)^6)dx. Apply the formula: \int a^ndx=\int newton\left(a^n\right)dx, where a^n=\left(3x^2+1\right)^6, a=3x^2+1, inta^n=\int\left(3x^2+1\right)^6, inta^ndx=\int\left(3x^2+1\right)^6dx and n=6. Expand the integral \int\left(729x^{12}+1458x^{10}+1215x^{8}+540x^{6}+135x^{4}+18x^2+1\right)dx into 7 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int729x^{12}dx results in: \frac{729}{13}x^{13}. The integral \int1458x^{10}dx results in: \frac{1458}{11}x^{11}.
