Question

Найти первообразную! Примеры на фото. 25 баллов.

Answer 1

Ответ:

$1)\ \ f(x)=9x^8+8x^7+15\ \ ,\ \ F(x)=x^9+x^8+15x+C\\\\\\2)\ \ f(x)=\dfrac{5}{2\sqrt{3x+2}}+\dfrac{1}{sin^24x}\ \ ,\ \ F(x)=\dfrac{5}{2}\cdot \dfrac{1}{3}\cdot 2\sqrt{3x+2}-\dfrac{1}{4}\cdot ctg4x+C\\\\\\F(x)=\dfrac{5}{3}\, \sqrt{3x+2}-\dfrac{1}{4}\, ctg4x+C\\\\\\3)\ \ f(x)=5sin\dfrac{x}{5}+cos2x\ \ ,\ \ F(x)=-25\, cos\dfrac{x}{5}+\dfrac{1}{2}\, sin2x+C$

$4)\ \ f(x)=10x^9+6x^5+5x\ \ ,\ \ F(x)=x^{10}+x^6+\dfrac{5x^2}{2}+C\\\\\\5)\ \ f(x)=\dfrac{6}{5\sqrt{4x+2}}+\dfrac{1}{cos^25x}\ \ ,\ \ F(x)=\dfrac{6}{5}\cdot \dfrac{1}{4}\cdot 2\sqrt{4x+2}+\dfrac{1}{5}\cdot tg\, 5x+C\\\\\\F(x)=\dfrac{3}{5}\cdot \sqrt{4x+2}+\dfrac{1}{5}\cdot tg\, 5x+C\\\\\\6)\ \ f(x)=3cos\dfrac{x}{3}+sin3x\ \ ,\ \ F(x)=9sin\dfrac{x}{3}-\dfrac{1}{3}\, cos3x+C$