Mathematics

Evaluate the following integration w.r.t. $$x$$
 $$\int \left[\left(9-\dfrac{x}{8}\right)+(4x+5)^{3}\right]dx$$


SOLUTION
$$\displaystyle\int \left[\left(9-\dfrac{x}{8}\right)+(4x+5)^3\right]dx$$
$$=\displaystyle\int \left[\left(9-\dfrac{x}{8}\right)+64x^3+1)5+80x^2+100x\right]dx$$
$$=\displaystyle\int \left[134+\dfrac{799}{8}x+80x^2+64x^3\right]dx$$
$$=\displaystyle 134x+\dfrac{799}{16}x^2+\dfrac{80}{3}x^3+\dfrac{64}{4}x^4+C$$
$$=134x+\dfrac{799}{16}x^2+\dfrac{80}{3}x^3+16x^4+C$$
$$\therefore \displaystyle\int \left[\left(9-\dfrac{x}{8}\right)+(4x+5)^3\right]dx=134x+\dfrac{799}{16}x^2+\dfrac{80}{3}x^3+16x^4+C$$.
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Subjective Medium Published on 17th 09, 2020
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