Tentukan hasil pengintegralan berikut : a. integral (2x^2 + 3) dx b. integral (4x^8 + 2x^5 +3) dx c.... Question from @nurismhy

October 2018 1 9 Report

Tentukan hasil pengintegralan berikut :
a. integral (2x^2 + 3) dx
b. integral (4x^8 + 2x^5 +3) dx
c. integral 10 / x^4 dx
d. integral 5x-4 / x^3
e. integral x^4 akar x dx
f. integral 5x akar x^3 dx

NamakuDuck A. $\int (2x^{2}+3)dx=\frac{2}{3}x^{3}+3x+C$
b. $\int (4x^{8}+2x^{5}+3)dx=\frac{4}{9}x^{9}+\frac{1}{3}x^{6}+3x+C$
c. $\int \frac{10}{x^{4}}dx=\int 10x^{-4}dx=-\frac{10}{3}x^{-3}+C=-\frac{10}{3x^{3}}+C$
d. $\int \frac{(5x-4)}{x^{3}}dx$
Misalkan u(x) = (5x - 4) dan $dv=\frac{1}{x^{3}},v=-\frac{1}{2x^{2}}$ .
=> $\int udv=uv-\int vdu$
=> $\int \frac{5x-4}{x^{3}} = -(\frac{1}{2x^{2}})(5x-4)-\int -\frac{1}{2x^{2}}(5)dx$
=> $-\frac{5x-4}{2x^{2}}+\int \frac{5}{2x^{2}}dx$
=> $-\frac{5x-4}{2x^{2}}-\frac{5}{2x^{2}}+C=\frac{-5x+1}{2x^{2}}+C$
e. $\int x^{4}\sqrt{x}dx$
Misalkan u(x) = x⁴ dan dv = √x, v = $\frac{2}{3}x\sqrt{x}$
=> $\int udv=uv-\int vdu$
=> $\int x^{4}\sqrt{x}dx=\frac{2}{3}x^{5}\sqrt{x}-\int \frac{2}{3}x\sqrt{x}(4x^{3}})dx$
=> $\frac{2}{3}x^{5}\sqrt{x}-\frac{8}{3}\int x^{4}\sqrt{x}dx$
=> $\frac{2}{3}x^{5}\sqrt{x}-\frac{8}{3}(\frac{2}{11}x^{5}\sqrt{x})+C$
=> $\frac{22}{33}x^{5}\sqrt{x}-\frac{16}{33}x^{5}\sqrt{x}+C=\frac{6}{33}x^{5}\sqrt{x}+C$
f. $\int 5x\sqrt{x^{3}}dx=5\int\sqrt{x^{5}}dx=5(\frac{2}{7}x^{3}\sqrt{x})+C=\frac{10}{7}x^{3}\sqrt{x}+C$

5 votes Thanks 8