أجد التكامل: (( x))/(x) dx.

نفرض u= x، ومنه du=dx/x؛ إذن u du=- u+C=-( x)+C. التعويض هنا مباشر لأن مشتقة x موجودة كعامل 1/x.

التكامل بالتعويض: Mathematics Tawjihi question with answer

A Tawjihi Mathematics question (التكامل) with the answer and worked steps.

From the Tawjihi question bank: Mathematics · التكامل

أجد التكامل: $\int \frac{\sin(\ln x)}{x}\,dx$ .

التكامل بالتعويض

The answer

نفرض

u=\ln x

، ومنه

du=dx/x

؛ إذن

\int\sin u\,du=-\cos u+C=-\cos(\ln x)+C

.

Explanation

التعويض هنا مباشر لأن مشتقة

\ln x

موجودة كعامل

1/x

.

Let Zaki explain it another way

The answer above is completely free. When you sign in, Zaki can explain this question a different way, give you ten more like it on the same lesson, and track your progress in the subject.

Practise more like this

Keep going

All Mathematics questions Mathematics hub Official past papers

Sign up now and plan your post-results step with Zaki — no invented ministry dates.

Start with Zaki Start with Zaki