What is the integral of cos(x)+1/5 x ?

The integral of cos(x)+1/5 x is sin(x)+(x^2)/(10)+C

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integral of cos(x)+1/5 x

\int cos (x) + \frac{1}{5} x d x

sin (x) + \frac{x ^{2}}{10} + C

Solution steps

\int cos (x) + \frac{1}{5} x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int cos (x) d x + \int \frac{1}{5} x d x

\int cos (x) d x = sin (x)

\int \frac{1}{5} x d x = \frac{x ^{2}}{10}

= sin (x) + \frac{x ^{2}}{10}

Add a constant to the solution

= sin (x) + \frac{x ^{2}}{10} + C

7 x + 1

\int_{2}^{5} 8 x^{7} d x

\int_{1}^{6} \frac{3}{x ^{2}} d x

y = - \frac{1}{5} x^{2} - \frac{6}{5} x + \frac{7}{5}, (- 5, 5)

\int e^{x} \cdot sin (2 x) d x

What is the integral of cos(x)+1/5 x ?
The integral of cos(x)+1/5 x is sin(x)+(x^2)/(10)+C